A Modified Constant-Stress Coupon for Enhanced Natural ... · A Modified Constant-Stress Coupon for Enhanced Natural Crack Start during Fatigue Testing Executive Summary The Structural

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A Modified Constant-Stress Coupon for Enhanced Natural Crack Start during

Fatigue Testing

Witold Waldman, Robert Kaye and Xiaobo Yu

Aerospace Division Defence Science and Technology Group

DST-Group-TR-3252

ABSTRACT

This report details the development of a modified constant-stress coupon for use in fatigue testing. This novel coupon design has a significantly greater surface area along the notch boundary that is subjected to the peak stress, and it is useful in studies of the probabilistic growth of in-service fatigue cracks where fatigue life is governed by the most severe defect. The extended region of uniform stress is achieved by shape optimisation of the notch boundary, resulting in the elimination of the highly-localised stress concentration that is a characteristic feature of a traditional dog-bone coupon. The presence of an extensive region of uniform stress increases the incidence of fatigue cracking from small naturally-occurring surface imperfections or discontinuities, as well as more uniformly distributing the fatigue cracking over the region of constant stress. Stress intensity factors have also been computed for simulated crack growth trajectories for edge cracks starting at various locations distributed along the notch boundary. Use of the constant-stress coupon reduces the number of coupons that need to be tested in order to attain desired statistical confidence levels, leading to significant time savings and greatly reduced costs in conducting fatigue testing programs studying the initiation and growth behaviour of small cracks.

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Approved for public release

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Published by Aerospace Division Defence Science and Technology Group 506 Lorimer Street Fishermans Bend, Victoria 3207, Australia Telephone: 1300 333 362 Fax: (03) 9626 7999 © Commonwealth of Australia 2016 AR- 016-590 May 2016 APPROVED FOR PUBLIC RELEASE

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A Modified Constant-Stress Coupon for Enhanced Natural Crack Start during Fatigue Testing

Executive Summary

The Structural and Damage Mechanics Group in the Airframe Technology and Safety Branch of Aerospace Division has been deeply involved in research to develop and apply structural and damage mechanics methods and technologies to enhance the safety, availability, and reduce the cost of ownership of airframes in service with the Royal Australian Air Force. Included amongst its wide range of capabilities are a unique and novel shape optimisation technology for the repair and fatigue life enhancement of airframe components, advanced computational and analytical tools and methods for improved determination of fatigue and crack growth life of airframes, and integrated analytical and numerical modelling of both complete and local structures for the improved assessment of structural response and capability.

This report details the development of a modified constant-stress coupon for use in fatigue testing. A constant-stress coupon is a novel design that has a significantly greater surface area along the notch boundary that is subjected to the peak stress. This extensive region of uniform stress is achieved by shape optimisation of the boundary of the notch, resulting in the elimination of the highly-localised stress concentration that is a characteristic feature of a traditional dog-bone fatigue testing coupon. The shape optimisation method that has been used here is based on the advanced and powerful shape optimisation technique that has been pioneered by the Structural and Damage Mechanics Group, and which has recently been modified and ported to be used with the Abaqus finite element analysis software code.

As the constant-stress fatigue coupon design is being used in studies involving crack growth, an assessment of its performance from a fracture mechanics perspective was also conducted. This involved the detailed computation of crack-growth trajectories and stress intensity factors for through-thickness edge cracks emanating from points distributed along the shape-optimised notch boundary. An advanced two-dimensional boundary element analysis technique was used for these calculations. The results reported here will serve to permit comparison with the crack paths that occur during the fatigue testing of the coupons.

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The use of constant-stress fatigue coupons will significantly assist research into improving the fundamental understanding of the probabilistic growth of in-service fatigue cracks where the fatigue life is governed by the most severe defect. The presence of an extensive region of uniform stress will increase the incidence of fatigue cracking from small naturally-occurring surface imperfections or discontinuities, as well as potentially more uniformly distributing the fatigue cracking over the region of uniform stress. Use of the constant-stress coupon will reduce the number of coupons that need to be tested in order to attain desired statistical confidence levels, leading to significant time savings and greatly reduced costs in conducting fatigue testing programs to study the initiation and growth behaviour of small cracks. The outcomes of this research into fatigue cracking will be applied to the long-term structural integrity management of both ageing and new ADF airframes.

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Authors Witold Waldman Aerospace Division Mr Witold Waldman completed a BEng (with distinction) in Aeronautical Engineering at the Royal Melbourne Institute of Technology in 1981. He commenced work in Structures Division in 1982, at what was then the Aeronautical Research Laboratory. He has published a number of papers and reports, and his experience has focussed on stress analysis using finite element and boundary element methods, structural mechanics, fracture mechanics, computational unsteady aerodynamics, structural dynamics testing, digital filtering of flight test data, nonlinear optimisation, and spectral analysis. His recent work has been in the areas of structural shape optimisation and the computation of stress intensity factors. He is currently a Senior Research Engineer in the Structural and Damage Mechanics Group in the Airframe Technology and Safety Branch of Aerospace Division within the Defence Science and Technology Group.

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Robert Kaye Aerospace Division Mr Robert Kaye joined what was then the Structures Division of the Aeronautical Research Laboratory in 1990 as a structural engineer with a background in full-scale testing. The first three years at DSTO were spent in evaluation of bonded repairs primarily using finite element methods. Included in that was the analysis of repairs to fuselage skin lap-joints, wing skin planks and bulkhead frames. More recently, he has been involved with structural and mechanical aspects of full-scale fatigue test installations. In particular, he played a key role in the development of a low-stiffness air-spring for the application of static load to a vibrating airframe. This work was followed by a period of several years doing research and development into the alleviation of stress concentrations by way of adaptive shape optimisation. This has been applied to concave metallic free boundaries and to the adhesive layer and end tapering of boron patches bonded to metallic structure. Upon his retirement, he is now a DST Honorary Fellow in Aerospace Division.

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Xiaobo Yu Aerospace Division Dr Xiaobo Yu completed a BEng in Naval Architecture Engineering in 1988, and a MEng in Structural Mechanics in 1991, both from Shanghai Jiao Tong University; and a PhD in Civil Engineering from the University of Sydney. He has held a lecturing position in Shanghai Jiao Tong University and several senior research positions in the University of Sydney and the University of NSW, and was also attached to Pacific Engineering Systems International as a CRC-ACS Visiting Research Fellow. In 2007 he joined what was then the Defence Science and Technology Organisation, and he is currently Science Team Leader for Structural Mechanics in Aerospace Division. In the context of airframe safety and life assessment and life extension, his main interests and responsibilities include structural shape optimisation, computational structural analysis and multi-axial fatigue.

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Contents 1. INTRODUCTION .......................................................................................................................... 1

2. STRESS ANALYSIS OF TYPICAL DOG-BONE COUPONS WITH NON-OPTIMAL NOTCH PROFILES ................................................................................................... 3 2.1 Notch with large 100-mm constant-radius arcs .................................................................. 3 2.2 Notch with constant central width and large constant 100-mm radius fillets ............... 4 2.3 Notch with constant central width and moderate constant 30-mm radius

fillets 5

3. PRIOR OPTIMAL CONSTANT-STRESS NOTCH PROFILE .............................................. 5

4. DESIGN OF THE MODIFIED COUPON WITH OPTIMAL CONSTANT-STRESS NOTCH PROFILE .......................................................................................................... 7 4.1 Nominal geometry and material properties ....................................................................... 7 4.2 Initial finite element mesh ..................................................................................................... 8 4.3 Performing the shape optimisation ...................................................................................... 8 4.4 Raw results of shape optimisation........................................................................................ 8 4.5 Preparation of raw optimal shape for manufacture ........................................................... 9

5. 2D FRACTURE MECHANICS ASSESSMENT OF MODIFIED CONSTANT-STRESS COUPON ....................................................................................................................... 12 5.1 Analysis of uncracked coupon ............................................................................................ 12 5.2 Computation of crack trajectories for edge-cracked coupon .......................................... 13 5.3 Computation of Beta factors for through-thickness edge-cracked coupon .................. 13 5.4 Computation of Beta factors for other crack geometries ................................................. 14

6. CONCLUSION ............................................................................................................................. 15

7. ACKNOWLEDGEMENT ............................................................................................................ 15

8. REFERENCES ............................................................................................................................... 16

APPENDIX A: FADD2D INPUT FILE FOR UNCRACKED NOTCH COMPOSED OF LARGE 100-MM CONSTANT-RADIUS ARCS ..................................... 35

APPENDIX B: FADD2D INPUT FILE FOR UNCRACKED NOTCH WITH CONSTANT CENTRAL WIDTH AND LARGE 100-MM RADIUS FILLETS ................. 36

APPENDIX C: FADD2D INPUT FILE FOR UNCRACKED NOTCH WITH CONSTANT CENTRAL WIDTH AND MEDIUM 30-MM RADIUS FILLETS .............. 38

APPENDIX D: FORTRAN 90 SOURCE CODE FOR THE CREATEDOGBONECOUPONMODEL PROGRAM ........................................................... 40

APPENDIX E: INPUT DECK USED TO CREATE FADD2D MODEL OF ORIGINAL CONSTANT-STRESS COUPON USING CREATEDOGBONECOUPONMODEL PROGRAM ........................................................... 49

APPENDIX F: FADD2D INPUT FILE FOR MODIFIED CONSTANT-STRESS COUPON WITH ONE CENTRALLY-LOCATED THROUGH-THICKNESS EDGE CRACK .............................................................................................................................. 50

APPENDIX G: IGES FILE OF COORDINATES FOR MODIFIED CONSTANT-STRESS COUPON ....................................................................................................................... 65


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Nomenclature a crack length E Young’s modulus of the material F boundary correction factor (beta factor) K stress intensity factor Kt net-section stress concentration factor Ktg gross-section stress concentration factor S local tangential stress at notch surface S∞ remote uniaxial tension stress x x-coordinate y y-coordinate σ stress along notch boundary σmax maximum tangential stress υ Poisson’s ratio of the material


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1. Introduction Prior work in DST Group by McDonald (1999a) has involved the computation of stress concentration factors (SCFs) for various fatigue test coupon profiles composed of straight lines and circular arcs. These coupons were required for use in fatigue testing to aid in the fatigue life management of RAAF airframes. To help maximise test machine usage efficiency and to provide the necessary statistical data for accurate estimation of fatigue life, it was desirable to test many short cracks on a single specimen. To achieve this, a test coupon was required that had a notch with a relatively large surface area of uniform stress (where the stress is constant within a specified small range). This led McDonald (1999b) to establish the design of an aluminium coupon that maximised the length of uniform stress under uniaxial tensile loading.

Following on from the work of Mattheck et al. (1992), the Structural and Damage Mechanics Group within DST Group has successfully developed and employed shape optimisation technology for the reduction of peak stresses occurring at typical stress concentrations such as fillets and holes (Heller, Kaye and Rose 1999; Waldman, Heller and Chen 2001; Burchill and Heller 2004; Heller et al. 2009, Waldman 2015). In essence, the method relies on adding material where stresses are high and removing material where stresses are low. Waldman and Heller (2006, 2015) have also significantly extended this in-house shape optimisation capability in order to be able to address problems that involve the simultaneous reduction of multiple stress peaks. The implementation of the method for use with the MSC Nastran finite element analysis (FEA) code that was developed by Braemar (2005) has also recently been ported by Kaye and Waldman (2016) to make use of the Abaqus FEA code running on a Linux–based computer system.

A distinct characteristic of shape-optimal designs is the presence of one or more large regions of uniform stress along the stress concentrator boundary, where the stress is constant within a small tolerance. Hence, in DST Group, Westcott (2010) and Kaye (2010) have previously taken advantage of this feature by applying shape optimisation methods to design specialised fatigue test coupons that have extensive regions of uniform stress. These shape-optimised coupon geometries are characterised by having the desired extensive regions of nearly-constant stress along a large proportion of the notch boundary, with the peak stress in the coupon corresponding to the stress level that is associated with the region of uniform stress.

The advantage offered by a constant-stress fatigue coupon is that there is a much larger area along the notch surface that is subjected to the peak stress, as the highly-localised stress concentration produced by a traditional dog-bone coupon is eliminated. It is therefore anticipated that the incidence of fatigue cracking from small naturally-occurring surface imperfections or discontinuities will be duly increased, as well as potentially being more uniformly distributed over the region of constant stress. This can serve to reduce the number of coupons that need to be tested, resulting in significant time savings and greatly reduced costs in conducting fatigue testing programs. The desired outcome from such


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fatigue tests is to improve the fundamental understanding of the probabilistic growth of fatigue cracks from small naturally-occurring defects, where the in-service fatigue life of the component is assumed to be governed by the most severe defect that is present (Cetin, Härkegård and Naess 2013). In addition, Molent, Barter and Wanhill (2011) and Barter, Molent and Wanhill (2012) have noted that surface imperfections and discontinuities are features that are inherent to the material and the manner of production of the component, and that the existence of such defects in typical aircraft alloys leads to fatigue cracking in tests of both coupons and components.

As a result of the novel properties offered by a constant-stress fatigue test coupon, such designs have recently begun to be extensively utilised by the Aircraft Forensic and Metallic Technologies Group within DST Group (Shekhter et al. 2015; Loader, Shekhter and Turk 2015; Loader et al. 2016; Niclis and Harrison 2016; Shekhter et al. 2016; Turk 2016a; Turk 2016b; Turk and Niclis 2016). Prior to this, in conducting their fatigue test program on multiple coupons that have a low SCF (low-Kt), Yu et al. (2014) have noted that, over a region of low stress concentration, the lead crack that dictates the fatigue life is often the fastest growing crack that starts from one of the worst discontinuities. They referred to this phenomenon as “natural crack start”, which cannot be reproduced using traditional dog-bone coupons such as those defined in ASTM (2012), because the stress concentration that is inherent in the design of those coupons is significant enough to dictate the starting positions of the fatigue cracks. Yu et al. (2014) have also noted a further limitation, in that, by confining the crack starting locations to the area of higher stress, fewer initial discontinuities and local material properties are sampled, which affects the growth of small cracks. As a result, the largest crack that eventually results in failure may start from a less severe discontinuity or grow at a slower rate. Also, when the largest crack starts from a location that is next to, but not exactly at, the peak stress location, the use of nominal peak stress overestimates the actual fatigue driving force. Consequently, Yu et al. (2014) have concluded that the fatigue test results obtained from traditional types of dog-bone coupons will exhibit more scatter in total fatigue life, and any distribution of life data would be skewed to a longer life, when compared to those on an actual aircraft structure.

The effectiveness of the prior optimal coupon design has been confirmed by Yu et al. (2014) through experimental strain measurement as well as fatigue tests under spectrum loading. However, as designed, these coupons have on occasion experienced undesirable premature failures in the grip region during other subsequent test programs. These failures typically occurred while undertaking testing at low load levels, with commensurately long specimen fatigue lives. A significant factor contributing to these failures is considered to be the use of oversized test specimen grips, which affect the gripping action. This is thought to produce fretting damage, which then leads to instances of fatigue failure in the region where the coupon is being clamped by the grips. Therefore, it became apparent that a need exists for the design of a Modified Constant-Stress Coupon with a view to reducing the incidence of coupon failures originating in the grip area. The performance of the coupon whose design is reported on herein is expected to be better because of the increased width of the new coupon in the grip area. It must also be kept in


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mind that the previous fatigue testing work undertaken with the narrower specimen has already produced an extensive usable body of results. In order to maintain compatibility with those results, it is desirable that the length of the constant-stress region in the modified coupon be very similar to that of the original design. This Report documents the design of this new Modified Constant-Stress Coupon.

In order to provide some background that serves as a basis for comparison, Section 2 gives the results of analyses of a variety of typical non-optimal non-constant stress dog-bone coupon designs. One of those designs has in fact previously been used in a coupon fatigue testing program in the DST Group. Section 3 then goes on to provide the results of a stress analysis of the original constant-stress coupon design. The design of the new Modified Constant-Stress Coupon is then described in Section 4. The results of a detailed fracture mechanics analysis of potential cracking along the notch boundary of the new coupon are presented in Section 5, and it includes simulated crack-growth trajectories and associated stress intensity factors for through-thickness edge cracks of various lengths. Finally, the conclusion is presented in Section 6.

2. Stress analysis of typical dog-bone coupons with non-optimal notch profiles

It is considered useful to develop a better quantitative understanding of the stress distribution in the notch region of some typical dog-bone axial fatigue test coupon geometries. For this purpose, a number of two-dimensional ¼-symmetry boundary element models of coupon designs are created here and analysed using the FADD2D boundary element code (Chang and Mear 1995; Newman et al. 2006). The assumed linear-elastic material properties for these aluminium coupons are a Young’s Modulus of E = 72.4 GPa and a Poisson’s ratio of υ = 0.33. Each model is subjected to a uniform uniaxial tensile load of 100 MPa applied to the ends of the specimen, and this was deemed to be capable of providing stress results in the notch region (the area of interest) comparable to those that would be expected if the actual grip loading could be more accurately simulated. Plane stress conditions were assumed in the analysis, which was deemed to be reasonable as the thickness of these coupons is small relative to the other dimensions.

2.1 Notch with large 100-mm constant-radius arcs

In prior DST Group work reported much earlier by McDonald (1999a), a simple notch design was developed that utilised a circular arc of large constant radius to produce a notch profile. The purpose behind this design was to try to minimise the stress concentration effect associated with the notch. This type of notch design is shown in Figure 1, and the hatched areas represent the grip length of 40 mm that had been adopted. The coupon dimensions for this notch design were: notch radius = 100 mm, total coupon


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length = 160 mm, width = 40 mm, thickness = 6.35 mm, notch half-length = 38 mm, notch depth = 7.5 mm, and net section half-width = 12.5 mm.

A FADD2D ¼-symmetry model was created and analysed using the previously specified linear elastic material properties for aluminium (see Appendix A for a listing of the input deck, which is also located in Objective folder fAV1044714). The FADD2D-computed normalised stress response along the notch boundary, σ/σmax, is shown in Figure 2. Here σ is the tangential stress, and σmax is the maximum tangential stress. The net-section SCF is Kt = 1.081 for this design, which compares very well with Kt = 1.082 obtained from a 3D analysis using the StressCheck finite element code (McDonald 1999a). The gross-section SCF is Ktg = 1.730. The stress response obtained here consists of a broad peak, centred on x = 0 mm. These results show that the stress changes by 8% over approximately 30 mm of the notch length (–15 mm ≤ x ≤ +15 mm), and by 33% over approximately 60 mm of the notch length (–30 mm ≤ x ≤ +30 mm). Hence, it is evident that the constant-radius specimen design cannot meet the requirement of having a significant region with uniform stress.

2.2 Notch with constant central width and large constant 100-mm radius fillets

An alternative dog-bone coupon notch design that is composed of a long constant-width centre section with transitioning fillets of large constant 100-mm radius is shown in Figure 3. This dog-bone coupon geometry was selected on the basis that it is similar to those that are used in many fatigue testing programs, often with circular through-thickness holes added to the centre section. The geometry shown in Figure 3 is expected to result in a considerable constant-stress zone in the central constant-width region. However, it is also anticipated that a significant stress concentration will occur in the fillet regions.

A ¼-symmetry 2D model of the geometry shown in Figure 3 was created and analysed using the FADD2D boundary element program (see Appendix B for a listing of the input deck, which is also located in Objective folder fAV1044714). The previously specified linear elastic material properties for aluminium were used, and the applied load once again consisted of a uniform uniaxial tensile load of 100 MPa. The computed normalised stress response along the notch boundary, σ/σmax, is shown in Figure 4. The net-section SCF for this coupon design is Kt = 1.071, while the gross-section SCF is Ktg = 1.714. It is noted that the stress response has a broad peak, located at about x = ±23.9 mm. The stress is quite constant over approximately 30 mm of the notch length in the central region of the coupon (–15 mm ≤ x ≤ +15 mm), albeit at a value of about σ/σmax = 0.93, which is 7% lower than the peak stress. The left and right peaks (from symmetry) in the stress distribution along the notch boundary occupy about 40 mm of the total notch length (–35 mm ≤ x ≤ –15 mm and +15 mm ≤ x ≤ +35 mm). Although this design has a considerable zone of constant stress in its central region, the presence of the significant peak in the stress distribution would be expected to result in crack growth in that particular area during fatigue testing, rather than in the zone of constant stress.


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2.3 Notch with constant central width and moderate constant 30-mm radius fillets

Another dog-bone coupon notch design, this time composed of a constant-width centre section with transitioning fillets of moderate constant 30-mm radius, is shown in Figure 5. These fillets have a much smaller radius than the 100-mm radius fillets used in the previous section and, as a result, they are expected to produce a more severe stress concentration effect.

A FADD2D ¼-symmetry 2D model of this geometry was created and analysed using the previously specified linear elastic material properties for aluminium (see Appendix C for a listing of the input deck, which is also located in Objective folder fAV1044714). The applied load once again consisted of a uniform uniaxial pressure of 100 MPa. The computed normalised stress response along the notch boundary, σ/σmax, is shown in Figure 6. The net-section SCF for this design is Kt = 1.240, while the gross-section SCF is Ktg = 1.984. These values are considerably more severe than those obtained when the 100-mm radius fillets were used. The stress response has a broad peak, located at about x = ±23.5 mm. The stress is quite constant over approximately 30 mm of the notch length in the central region of the coupon (–15 mm ≤ x ≤ +15 mm), albeit at a value of about σ/σmax = 0.80, which is 20% lower than the peak stress. The left and right peaks (from symmetry) in the stress distribution occupy about 40 mm of the total notch length (–31 mm ≤ x ≤ –15 mm and +15 mm ≤ x ≤ +31 mm). Although this design has a considerable zone of constant stress in its central region, the presence of the significant peak in the stress distribution would be expected to result in crack growth originating somewhere in that particular area during fatigue testing, rather than in the zone of constant stress.

3. Prior optimal constant-stress notch profile Some years ago now, the original DST Group shape optimisation code was ported to work with the MSC Patran and Nastran finite element analysis software, and the specifics of this version of the code are covered by Braemar (2005). The process used for preparing an optimal shape for manufacture is described by Wescott and Heller (2009). Taken in combination, these procedures were used by Wescott, Jones and Heller (2010) and then Kaye (2010) to design the original constant-stress fatigue test coupon.

The first constant-stress specimen was designed by Wescott, Jones and Heller (2010) using 2D shape optimisation techniques, as the then implementation of the code was not working correctly for 3D open boundary problems. Their specimen was 6.35 mm thick and had a nominal grip area of 40×40 mm at each end. The grip load was modelled as a constant traction (tangential pressure) during the optimisation process, and was implemented using nodal forces. A short 5 mm buffer zone between the grip line and the end of the notched section was included. As the specimen is 160 mm in total length, this


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results in a notch length of 70 mm. The minimum section width was 24 mm at the centre of the specimen, corresponding to a notch depth of 8 mm. Minimum radius of curvature constraints in the range 5 mm to 25 mm were investigated, and a value of 20 mm was chosen for the production version of this design. The net-section Kt was 1.03 and the length of notch profile with up to 2% stress variation was 50 mm.

After correcting a bug in the code, Kaye (2010) subsequently ran a 3D version of the shape optimisation algorithm, which for the unsmoothed optimal notch shape produced a net-section Kt of 1.03. This specimen, which is shown in Figure 7, differed slightly from the earlier one, in that the depth of the notch was 7.5 mm rather than 8 mm. The total arc length of the constant-stress region along each notch is about 55.5 mm, falling within the region –27.5 mm ≤ x ≤ +27.5 mm. The uniformity of the stress in the constant-stress zone was found to be very good, to within a small fraction of one per cent.

As mentioned by Kaye (2010), the 5 mm buffer zone between the grip region and the end of the notch was chosen because a discontinuity occurs at the edge of the grip. The exact stress/strain state at this location is unknown, as it depends on the amount of surface yielding and/or slip that occurs over the grip area contact surface. Preliminary finite element analyses conducted by Wescott, Jones and Heller (2010) had also shown that excessive local stresses occur near the ends of the notch if a suitable buffer zone is not included.

A FADD2D ¼-symmetry 2D model of the Kaye (2010) coupon was created and analysed using the previously specified linear elastic material properties for aluminium. An initial FADD2D input deck was created using a custom-written Fortran 90 program called CreateDogboneCouponModel (see Appendix D for the source code listing of this program, and Appendix E for the associated input deck, both of which are also located in Objective folder fAV1044714). Note that the coordinates of the notch profile that were used here were those that had been obtained after the radius-of-curvature coordinate-smoothing process described by Wescott and Heller (2009) had been applied. The applied load once again consisted of a uniform uniaxial pressure of 100 MPa. The initial input deck was manually edited to convert it from a full model to the desired ¼-symmetry model.

The computed normalised stress response, σ/σmax, along the smoothed notch boundary is shown in Figure 8. The net-section SCF for this design is Kt = 1.038, which is in good agreement with the prior result of Kt = 1.030 that was reported by Kaye (2010), and the gross-section SCF is Ktg = 1.660. The normalised stress is quite constant over an arc length of approximately 54.4 mm along the notch in the central region of the coupon (–27.0 mm ≤ x ≤ +27.0 mm). Although the stress response is very flat, the stress level in this region is about 0.7% lower than the peak stress, which occurs at about x = 25.5 mm. This is likely to be a consequence of a number of interacting factors. Firstly, the smoothing process, which has been applied to produce the smoothed notch boundary, has a small detrimental impact on the uniformity of the boundary stresses, as originally noted by Kaye (2010) and subsequently further investigated by Evans, Yu and Heller (2015). Secondly, first-order


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elements were used in the original Nastran-based shape optimisation, whereas the FADD2D code utilises 2nd-order boundary elements that are capable of more accurately resolving local stress variations associated with any given geometry. Finally, the optimal shape is based on a 3D finite element analysis, whereas the FADD2D analysis is 2D in nature.

4. Design of the modified coupon with optimal constant-stress notch profile

The prior constant-stress coupon design has experienced undesirable failures in the grip area during the fatigue test program, and a contributing factor is considered to be the use of oversized grips. By increasing the width of the coupon in the grip area, while maintaining the minimum width in the central region, it is expected that failures in the grip area will be avoided. As the previous fatigue testing work has already produced a quantity of results, it is required to create a new coupon design that maintains as much compatibility with those results as possible. In that respect, it is desired that the length of the constant-stress region in the modified coupon be very similar to that of the original design.

The previous MSC Patran/Nastran–based DST Group shape optimisation procedure has recently been modified for use with the Abaqus finite element analysis code by Kaye and Waldman (2016). This new version of the shape optimisation code was used here for designing the new Modified Constant-Stress Coupon. The Abaqus-based procedures are presently capable of performing a 2.5D optimisation analysis. This means that the y-displacement through the thickness of the model is maintained at each point on the notch profile while the profile is being optimised.

4.1 Nominal geometry and material properties

The nominal design of the Modified Constant-Stress Coupon is shown in Figure 9, and it is based on the previous design for a constant-stress coupon reported in Kaye (2010). As before, the new coupon is 6.35 mm thick, and has linear-elastic material properties typical of an aluminium alloy: E = 72.4 GPa and υ = 0.33. To improve the performance in the grip area, the gross width of the new coupon has been increased to 60 mm, with a gripped area that is now 60 mm × 60 mm at each end. The new design also includes a 25-mm buffer zone between the grip line and the end of the notched region, whereas it was 5 mm in the previous design described by Kaye (2010). The increased size of this buffer zone is expected to make the stresses less sensitive to different boundary conditions that might be utilised to simulate the grip loading. The total length of the new coupon is 244 mm. The minimum cross-sectional width in the notched region is the same as before (25 mm). As the notch depth in this Modified Constant-Stress Coupon is more severe than previously, the length of the notch region was increased from 70 mm to 74 mm. This will ostensibly


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provide additional room over which the constant stress zone can develop, thus offsetting to some degree the effects of the more severe stress concentration geometry.

4.2 Initial finite element mesh

In order to perform the shape optimisation, it is necessary to create an initial finite element model. A ⅛-symmetry model of the coupon was developed in order to reduce computation time and to avoid potential numerical errors. The model was created using the MSC Patran pre- and post-processing software, and then an Abaqus input deck was written out. Figure 10 shows a general view of the 3D finite element mesh that was created. The model utilised six layers of 8-noded hexagonal elements through the half-thickness.

A side view of the finite element model with the optimisation zone highlighted is shown in Figure 11. The assumed starting shape of the notch is a straight line, which was subdivided into 80 segments of equal length. The grip load was modelled as a uniformly-distributed constant traction force, and it was implemented using nodal forces. For this linear-elastic model, the applied uniaxial traction load was equivalent to a force of 50.02 kN (calculated by summing up the individual contributions of the forces applied at the nodes). This leads to a gross-section average stress of 131.3 MPa, and a net-section average stress of 315.1 MPa.

As we will be performing a linear elastic stress analysis, the load level can be scaled to obtain suitable stress levels in the notch zone to suit the particular requirements of the fatigue test.

4.3 Performing the shape optimisation

Prior to performing the shape optimisation, some further processing of the initial Abaqus input deck was conducted in accordance with the method described by Kaye and Waldman (2016) in order to prepare it for use by the shape optimisation code. The entire notch region was chosen as the movable boundary during the optimisation process (see Figure 11). The nodal movement at each point along the notch boundary was calculated using the maximum through-thickness stress. A minimum radius of curvature constraint of 20 mm was applied. All seven nodes through the thickness at each location on the notch boundary were moved by the same amount at each iterative step. The optimisation process was allowed to proceed for 400 iterations, whereupon it was manually terminated.

4.4 Raw results of shape optimisation

The resulting raw shape for the optimised constant-stress coupon that was produced by the shape optimisation process is shown in Figure 12. The contours of maximum principal stress from the finite element analysis are shown in Figure 13. The distribution of normalised principal stress, σ/σmax, along the notch boundary is shown in Figure 14, where σ is the largest principal stress through the thickness at each location, and σmax is the


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maximum value of the principal stress along the optimised notch boundary. The peak occurs at the centre of the notch boundary, and is σmax = 330.3 MPa. Using this value of stress, the gross-section SCF is Ktg = 2.516 for this configuration, while the net-section SCF is Kt = 1.048.

Referring to Figure 14, it is noted that, as expected, the normalised maximum principal stress in the central region of the optimised notch boundary is very uniform. This constant-stress zone extends over an arc length of approximately 51.2 mm, falling within the region –25.3 mm ≤ x ≤ +25.3 mm. The standard deviation of the normalised principal stress in the constant-stress region is only 0.006%, which is negligible, indicating the optimality of the solution. The arc length of the present constant-stress region is 7.7% less than that of the original constant-stress coupon.

In Figure 15, the maximum principal stress contour levels were adjusted to lie between a maximum of 330.3 MPa and a minimum of 310.5 MPa, with 12 contour bands in between. Each of these contour levels represents a 0.5% change in stress relative to the peak stress, for a total range of 6.0%. To provide some details of a higher resolution, Figure 16 shows contours of maximum principal stress that lie within 1.0% of the peak value.

As depicted in Figures 13–16, the distribution of the principal stress is very uniform along a large section of the notch surface of the optimised boundary contour, just as required. Furthermore, the variation of the maximum principal stress in the thickness direction is generally very low, this being particularly so at the centre of the coupon. Through-thickness variation in the maximum principal stress only becomes noticeable near the end of the constant stress zone. As expected, the through-the-thickness stress distribution peaks at the mid-plane of the coupon.

4.5 Preparation of raw optimal shape for manufacture

As described by Wescott and Heller (2009), and more recently by Evans, Yu and Heller (2015), past experience with the numerically-controlled machining of free-form notch shapes has indicated that it is desirable to process the notch coordinates so that the shape of the notch can be represented by a series of many short circular arcs. This conversion procedure also incorporates the facility for performing some smoothing of the raw notch shape in order to reduce the variability of the radius of curvature (ROC) along the notch boundary. In practice, the shape transformation process produces only very minor adjustments to the raw shape, and the resulting shape is still essentially free-form. In addition, the ROC-smoothing process has a very small effect on the stress distribution along the notch profile, which although noticeable is often negligible. Experience with some optimal shapes appears to indicate that the ROC-smoothing process can result in stresses that increase slightly near the end of the zone of constant stress (see Figure 8 for an example of this type of behaviour).


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A plot of the ROC distribution computed from the nodal coordinates along the entire (mirrored) raw unsmoothed as-optimised notch boundary is shown in Figure 17. The ROC at any given node was computed by a fitting circular arc through the three sets of coordinates comprised of that node and its immediate left and right neighbours (except at the start and end nodes along the boundary). The effect of the ROC constraint of 20 mm is clearly visible at the two ends of the notch boundary. From the response displayed in Figure 17, it is apparent that there are significant fluctuations in the ROC, with a large number of very high ROC values being present. These large fluctuations in ROC value have been found to cause difficulties during the manufacturing of optimal shapes using standard computer numerically-controlled machining techniques.

The rapid and high-amplitude oscillations in the radius-of-curvature of the as-optimised geometry are potentially caused by the use of first-order elements during the iterative finite element analysis. Prior shape optimisation using second-order elements did not appear to display this rather unsatisfactory behaviour. Further investigation is warranted in order to remediate this problem. It is considered that it would be better not to apply the previously-developed automated smoothing procedures in a brute force manner. It would be preferable to determine the cause of the radius-of-curvature problems and address them directly.

Upon subsequent closer investigation here, these rapid and high-amplitude oscillations in the computed ROC values have been identified as being associated with very small transitions in slope between the edges of some of the linear 8-noded hexahedral first-order finite elements. These cause the large calculated ROC values associated with pairs of elements whose connected edges are nearly collinear. This behaviour is depicted in Figure 18, where the shape of the raw optimal profile near x = 0 mm has been plotted (solid line). The presence of these “flat” areas, with their commensurately-high ROC values (based on a 3-point circular arc curve fit), is clearly evident in the plot of the raw unsmoothed optimal profile. It is believed that these “flat” regions are caused by the numerical approximations inherent in the use of first-order finite elements to obtain the optimal solution, as prior shape optimisation solutions obtained using second-order finite elements did not display the type of oscillatory ROC behaviour found here (see Waldman, Heller and Chen 2001; Waldman and Heller 2006; Waldman and Heller 2015). The dashed line shows the results of fitting a smooth curve through every second point of the original data set, resulting in a smooth line that accurately follows the underlying shape of the optimal profile.

Hence, as in the prior work performed by Kaye (2010), it is necessary here to undertake ROC smoothing of the raw geometric coordinates of the optimised boundary shape in order to make the notch suitable for manufacturing. Based on an assessment of the relevant information presented in Figure 17 and Figure 18, it was decided to accomplish this smoothing by using a two-phase process in order to produce a result of sufficiently high quality.


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In the first phase of the smoothing process, the raw optimal shape was curve fit using Microsoft Excel, with the problem coordinates that produced the high-amplitude ROC values omitted from the fit. Those points were then manually modified to lie closer to the interpolated shape, thus greatly reducing the severity of the local ROC variations. The result of this process is depicted in Figure 19. There it is evident that the extreme ROC variations have been reduced quite significantly, producing a much smoother overall behaviour. This result is now much more in keeping with our expectations for an optimal shape, but some further smoothing of the ROC variations is still desirable.

In the second phase of the radius of curvature smoothing process, the techniques reported by Wescott and Heller (2009) were applied to further smooth the notch shape. Two cycles of this automated smoothing were computed, and the ROC results obtained are depicted in Figure 20. The (x, y) coordinates at the two ends of the notch, as well as the (x, y) coordinate associated with the centre of the notch shape, were held fixed during the ROC smoothing process. Because of the manual adjustment of the node coordinates prior to undertaking the next phase of ROC smoothing, the automated ROC smoothing process has been very effective in further reducing the variations in ROC along the notch boundary, even with just two cycles.

Note that this level of ROC smoothing has a very small effect on the stresses in the constant-stress zone. This was checked by creating a new finite element model based on the smoothed coordinates of the optimal boundary. The normalised maximum principal stress for the smoothed notch geometry is shown in Figure 21. Compared to the results for the unsmoothed shape, the corner at approximately x = 25 mm is slightly more rounded, and the extent of the constant stress zone has been reduced a little bit (from x = 25.3 mm to x = 24.8 mm). The arc length of the constant-stress zone for the smoothed notch is 50.3 mm, and this is 1.8% shorter than for the unsmoothed notch.

The smoothed notch coordinates are supplied in Table 1. These were read into MSC Patran and used to generate an IGES file containing a representation of the smoothed optimal notch profile suitable for use in creating commands for computer numerically controlled machining of the coupons. The IGES file format is used to specify the notch boundary as a series of circular arcs and straight line segments. A listing of the contents of the IGES file corresponding to the notch contour for the Modified Constant-Stress Coupon is provided in Appendix G (a copy of this file can also be found in Objective folder fAV1044714, and the name of the file is Al_mod_optimal_3D_msmth_smoothed_002.igs).

It is instructive to compare the smoothing approach used above with the results that are obtained when the original raw unsmoothed coordinates for the Modified Constant-Stress Coupon have been passed through 20 cycles of the automated ROC smoothing algorithm. The resulting ROC variation in the notch region is shown in Figure 22. It is apparent that these results are clearly different from those presented in Figure 20, with the major differences being confined to the central region of the notch, –7 mm ≤ x ≤ +7 mm. The ROC results obtained using 20 cycles of automated smoothing have a peak ROC value that is


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about 15% greater. It is considered here that the application of manual plus automated smoothing has produced a smoother overall result, and it is expected that the resulting changes to the shape coordinates will be less than those produced by 20 cycles of automated smoothing.

5. 2D fracture mechanics assessment of modified constant-stress coupon

As the Modified Constant-Stress Coupon will be used in fatigue testing studies involving crack growth, it is instructive to assess its performance from a fracture mechanics perspective. The programs that were used for this analysis are located in Objective folder fAV1044714.

5.1 Analysis of uncracked coupon

Firstly, a full 2D model of the uncracked Modified Constant-Stress Coupon was created for analysis with FADD2D using the coordinates of the node locations in the original finite element model. A full model was needed as this forms the basis for subsequent stress intensity factor calculations associated with the placement of through-thickness edge cracks at various assumed locations distributed along the notch boundary.

The material properties corresponded to those for a typical aluminium alloy, and were the same as before (E = 72.4 GPa and υ = 0.33). Plane stress conditions were specified as the thickness of the specimen is small compared to the other dimensions. The applied load consisted of a uniform tensile pressure applied to the vertical edges at the two ends. To prevent rotation of the grip ends, 6 points were chosen on the grip zone boundary and restrained from moving in the y-direction. Using the (x, y) coordinate system defined in Figure 9, these points were located at (x, y) = (±62 mm, 20 mm), (±62 mm, –20 mm) and (±122 mm, 0 mm). In addition, in order to prevent rigid body motion of the coupon, the point on the boundary at (x, y) = (–122 mm, 0 mm) was restrained from moving in the x-direction.

The FADD2D model was created using the CreateDogboneCouponModel program (see Appendix D), and it was used to compute the maximum principal stress along the optimised notch boundary of the modified constant stress coupon. Figure 23 plots the normalised maximum principal stress obtained from the boundary element model, and compares it to the results obtained from the finite element model that was used during the shape optimisation process. It is evident that the two quite different computational approaches have produced results that are very similar. Using the FADD2D boundary element method, the gross-section SCF is Ktg = 2.519, which is almost identical to the value Ktg = 2.516 obtained using the finite element method.


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5.2 Computation of crack trajectories for edge-cracked coupon

Using the 2D model described above, an edge crack was inserted at various locations along the notch boundary. As a result of the 2D nature of the solution, the edge crack is assumed to be a through crack. In each case, the initial crack length set to be 0.1 mm, which can be regarded as being a very short crack relative to the size of the specimen. At each chosen location, the simulated crack was oriented to be perpendicular to the boundary. This essentially means that the crack was initially aligned to open in a Mode I dominant crack propagation mode, as this was assumed to be representative of what might happen in the coupon during fatigue testing.

For the purposes of this analysis, the cracks are located at different points along the notch boundary with the following x-coordinates: 0.00 mm, 4.24 mm, 8.51 mm, 12.74 mm, 16.95 mm, 21.11 mm, 23.17 mm, 25.26 mm, 29.45 mm, and 32.14 mm. These starting points correspond to node locations in the original finite element model. The FADD2D code was used to compute the crack trajectory for a single crack growing from each of these locations. A crack growth increment of 0.1 mm per iteration was used to compute the crack growth trajectory associated with each cracking scenario. For the purpose of this simulation, the cracks were allowed to grow until they had reached 20 mm in length.

The computed crack trajectories obtained for each of the cracks are shown in Figure 24. The trajectories become more curved as the starting location of the crack moves further away from the centre of the coupon. The crack trajectories remain relatively straight in the range of starting locations 0 mm ≤ x ≤ 15 mm.

5.3 Computation of Beta factors for through-thickness edge-cracked coupon

When the crack trajectories were being computed, the FADD2D boundary element code was also calculating the corresponding stress intensity factors, K, for the particular crack geometry that was present at each crack growth increment. It is considered instructive to compare these stress intensity factors to those corresponding to an edge crack of equivalent length that is located in a semi-infinite plate.

For a through-thickness edge crack of length a in a semi-infinite plate subjected to a remote uniaxial tension stress, S∞, the equation for the stress intensity factor K is

FaSK π= ∞ (1)

where F is a boundary correction factor (also called a Beta factor). As its name implies, the boundary correction factor accounts for the influence of various boundaries, but it is also often a function of parameters such as crack geometry, crack length, plate width, plate thickness, hole radius (where present), angular position along a crack front, etc. However, for the semi-infinite plate geometry, the boundary correction factor is a constant value,


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and is simply F = 1.1215 (Tada, Paris and Irwin 2000; Broek 1978), which is also known as the free-edge correction factor.

For a through-thickness edge crack that is located at any point along the notch boundary of the Modified Constant-Stress Coupon, the stress intensity factor can be written as

FaSK π= (2)

where S is the local tangential stress at the notch surface, and a is the crack length as measured along the curved crack trajectory. In the constant stress region, S can be computed by using S = Ktg S∞, where Ktg is the local gross-section SCF and S∞ is the remote uniform uniaxial tension stress applied to the ends of the coupon.

Figure 25 shows the boundary correction factors, F, plotted as a function of crack length, a, for a number of cracks starting from different points along the notch boundary. As a point of reference, the crack-length-independent boundary correction factor for a through-thickness edge crack in a semi-infinite plate is represented by the dashed horizontal line (F = 1.1215). For cracks located in the range 0 mm ≤ x ≤ 16.95 mm that have crack lengths a ≤ 2.5 mm, it is apparent that the geometry factor is within about 2% or so of F = 1.1215 for an edge crack in a semi-infinite plate.

The boundary correction factors as a function of distance along the notch boundary for edge cracks of varying lengths for the Modified Constant-Stress Coupon are plotted in Figure 26. The boundary correction factor for very short cracks, a ≤ 0.1 mm, is within 1.0% of the theoretical edge crack solution, F = 1.1215, over the entire length of the constant stress region. For short cracks, a ≤ 1.0 mm, the boundary correction factor is within 3.3% of F = 1.1215 along 84% of the constant-stress region, dropping by 7.5% at the end of the constant-stress zone.

5.4 Computation of Beta factors for other crack geometries

From the data presented in Figure 25 and Figure 26, the stress intensity factors for short through-thickness edge cracks for the constant stress specimen are largely in agreement with the solution for an edge crack in a semi-infinite plate. By analogy, it would therefore be expected that stress intensity factors for other types of short cracks (e.g. circular or elliptical corner cracks, circular or elliptical surface cracks, etc.) would be well represented by their nominal solutions computed for geometries that are similar to that of the constant-stress coupon. For example, if so desired, the stress intensity factor equations for planar semi-elliptical surface and corner flaws published by Broek could be utilised (Broek 1978, Section 3.6, Elliptical cracks). Hence, for many types of small (short) natural flaws, the body of existing stress intensity factor solutions can be taken advantage of, thus circumventing the need for computation of new sets of solutions that are specific to the present coupon geometry and loading.


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6. Conclusion The coordinates of the smoothed notch profile for the new Modified Constant-Stress Coupon were presented in Table 1. These have also been made available as an IGES file, which can be utilised for manufacturing of the coupons using numerically-controlled machining equipment. A listing of the contents of the IGES file is given in Appendix G, and a copy of the file can be found in Objective folder fAV1044714 (the name of the file is Al_mod_optimal_3D_msmth_smoothed_002.igs).

A summary of the dimensions of the Modified Constant-Stress Coupon, together with those of the original design, is presented in Table 2. It is noted that the grip area of the Modified Constant-Stress Coupon has been increased by 225% over the original constant-stress coupon design. Together with the increase in gross-section SCF resulting from the increase in the total width of the coupon, the incidences of specimen failure in the grip zone are expected to be greatly reduced, if not entirely eliminated. The arc length of the constant-stress zone in the Modified Constant-Stress Coupon is approximately 7.5% less than that which was obtained for the original constant-stress coupon. If required, a closer match could be attained by increasing the length of the notch zone and/or reducing the depth of the notch.

Using a 2D boundary element model of the Modified Constant-Stress Coupon, a number of potential crack growth trajectories have been computed by using the FADD2D fracture analysis code to perform simulations of 2D through-thickness edge cracks. The starting locations of the edge cracks were distributed along the constant-stress zone of the notch boundary. As the cracking location moved away from the centre of the coupon, the computed crack trajectories progressively became more curved. In the event that cracks that develop in the coupons are allowed to grow to a long length, it would be interesting to compare the crack growth trajectories obtained from fatigue testing with their computationally-determined counterparts.

7. Acknowledgement The author would like to thank Professor Mark E Mear, University of Texas at Austin, and Professor James C Newman Jr, Mississippi State University, for providing access to the FADD2D boundary element analysis code that was utilised for the fracture mechanics calculations in this report.


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8. References ASTM E606/E606M-12, Standard Test Method for Strain-Controlled Fatigue Testing, ASTM International, West Conshohocken, PA, 2012, www.astm.org.

Barter SA, L Molent, RJH Wanhill. Typical fatigue-initiating discontinuities in metallic aircraft structures. International Journal of Fatigue, Vol 41, 2012, pp 11–22.

Braemar R. Code enhancements for the Patran/Nastran structural optimisation. DSTO Minute, File B2/129/Pt4, Melbourne, 20 May 2005.

Broek D. Elementary Engineering Fracture Mechanics, Second Edition. Sitjhoff & Noordhoff, The Netherlands, 1978.

Burchill M, M Heller. Optimal notch shapes for loaded plates. Journal of Strain Analysis for Engineering Design, Vol 39, No 1, 2004, pp 99–116.

Cetin A, G Härkegård, A Naess. The fatigue limit: An analytical solution to a Monte Carlo problem. International Journal of Fatigue, Vol 55, 2013, pp 194–201.

Chang C, ME Mear. A boundary element method for two dimensional linear elastic fracture analysis. International Journal of Fracture, Vol 74, 1995, pages 219–251.

Evans R, X Yu, M Heller. Transfer effects for stress optimal shapes between design codes and from design to NC manufacture. 11th World Congress on Structural and Multidisciplinary Optimisation, 7–12 June, 2015, Sydney Australia.

Heller M, M Burchill, R Wescott, W Waldman, R Kaye, R Evans, M McDonald. Airframe life extension by optimised shape reworking – Overview of DSTO developments. 25th ICAF Symposium – Rotterdam, 27–29 May 2009.

Heller M, R Kaye, LRF Rose. A gradientless finite element procedure for shape optimization. Journal of Strain Analysis, Vol 34, No 5, 1999, pp 323–336.

Kaye R. Follow-on analysis of uniform stress coupons for combat aircraft life assessment. DSTO Minute, File B2/129/Pt4, 16 December 2010.

Kaye R, W Waldman. Conversion of DST Group shape optimisation software for increased portability across computing platforms. DST Group Technical Report, 2016 (DST-Group-TR-3251).

Loader C, A Shekhter, S Turk. Assessment of the effect of anodizing on fatigue life of aluminium alloys using equivalent crack size modelling methods. Aging Airworthiness Aircraft and Sustainment Conference, Brisbane, 2015.

Loader C, A Shekhter, S Turk, J Niclis, K Sharp. Investigation into the effect of sulphuric acid anodising on the fatigue life of AA7050-T7451. DST Group Technical Report, 2016 (to be published).


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Mattheck C, D Erb, K Bethge, U Begemann. Three-dimensional shape optimisation of a bar with a rectangular hole. Fatigue & Fracture of Engineering Materials & Structures, Vol 15, Issue 4, April 1992, pp 347–351.

McDonald M. FEA-COUPON-001 (OPT), Rev 2, Coupons Stress Analysis. DSTO Internal Document, 12 June 2009a.

McDonald M. FEA-COUPON-002 (OPT), Rev 1, Optimal shapes for coupons. DSTO Internal Document, 9 June 2009b.

Molent L, SA Barter, RJH Wanhill. The lead crack fatigue lifing framework. International Journal of Fatigue, Vol 33, Issue 3, 2011, pp 323–331.

Newman Jr JC, C Chang, L Xiao, ME Mear, VJ Kale. FADD2D: Fracture Analysis by Distributed Dislocations, Version 1.0, User Guide for Personal Computers with Demonstration Example. October 2006.

Niclis J, T Harrison. Fatigue Implications of surface treated AA7050-T7451 tested under VA loading. DST Group Technical Report, 2016 (to be published).

Shekhter A, C Loader, S Turk, PK Sharp. Effect of anodising treatments on equivalent crack size of the 7XXX aluminium alloy. 16th Australian International Aerospace Congress, 23–24 February 2015, Melbourne, Australia.

Shekhter A, C Loader, S Turk, J Niclis. Fatigue implications of surface treated AA7085-T7452 tested under CA and VA loading. DST Group Technical Report, 2016 (to be published).

Tada H, PC Paris, GR Irwin. The Stress Analysis of Cracks Handbook. Third Edition, Professional Engineering Publishing, 2000.

Turk S, J Niclis. Microstructural and fractographic assessment of fatigue crack behaviour of surface treated AA7085-T7452. DST Group Technical Report, 2016 (to be published).

Turk S. Fatigue Implications of sulphuric acid anodising on AA7050-T7451 aluminium alloy. 10th International Conference on Structural Integrity and Failure (SIF-2016): Advances in Materials and Structures, 12–15 July 2016a, Adelaide, Australia (to be presented).

Turk S. Fractographic analysis and fatigue crack growth of surface treated AA7050-T7451 coupons. DST Group Technical Report, 2016b (to be published).

Waldman W, M Heller, GX Chen. Optimal free-form shapes for shoulder fillets in flat plates under tension and bending. International Journal of Fatigue, Vol 23, 2001, pp 509–523.

Waldman W, M Heller. Shape optimisation of holes for multi-peak stress minimisation. Australian Journal of Mechanical Engineering, Vol 3, No 1, 2006, pp 61–71.


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Waldman W, M Heller. Shape optimisation of holes in loaded plates by minimisation of multiple stress peaks. DSTO Research Report DSTO-RR-0412, April 2015.

Waldman W. Determination of minimised Kt values and boundary shapes for a class of quasi-rectangular holes in infinite plates. DST Group Technical Report TR-3125, July 2015.

Wescott R, M Heller. Transforming stress optimal free form shapes for improved numerically controlled manufacture. DSTO Research Report DSTO-RR-0340, July 2009.

Wescott R, M Jones, M Heller. Stress analysis for design of uniform stress coupons for combat aircraft life assessment. DSTO Minute, File B2/129/Pt4, 14 July 2010.

Yu X, M Burchill, R Kaye, S Barter. Optimal coupon design to achieve natural crack start in coupon fatigue tests. In: Recent Advances in Structural Integrity Analysis: Proceedings of the International Congress (APCF/SIF-2014). Editors: L Ye, A Kotousov, L Chang. Darlington Campus, University of Sydney, Australia, 9–12 December 2014, pp 137–141.


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Table 1: Coordinates of the smoothed optimal profile for Modified Constant-Stress Coupon. (See Figure 9 for definition of the x-y coordinate system.)

Point x (mm) y (mm) Point x (mm) y (mm) 1 0.0000 12.5000 42 22.7246 15.0170 2 0.5594 12.5011 43 23.2598 15.1800 3 1.1188 12.5044 44 23.7921 15.3519 4 1.6782 12.5098 45 24.3211 15.5338 5 2.2376 12.5175 46 24.8464 15.7263 6 2.7969 12.5273 47 25.3673 15.9302 7 3.3562 12.5394 48 25.8825 16.1481 8 3.9154 12.5538 49 26.3911 16.3812 9 4.4746 12.5704 50 26.8926 16.6292

10 5.0337 12.5894 51 27.3867 16.8914 11 5.5927 12.6109 52 27.8732 17.1676 12 6.1516 12.6347 53 28.3515 17.4577 13 6.7104 12.6612 54 28.8213 17.7614 14 7.2691 12.6902 55 29.2822 18.0785 15 7.8276 12.7218 56 29.7337 18.4088 16 8.3860 12.7562 57 30.1754 18.7522 17 8.9442 12.7935 58 30.6069 19.1082 18 9.5021 12.8336 59 31.0278 19.4766 19 10.0599 12.8767 60 31.4378 19.8572 20 10.6174 12.9230 61 31.8365 20.2497 21 11.1746 12.9726 62 32.2235 20.6537 22 11.7315 13.0254 63 32.5984 21.0688 23 12.2881 13.0817 64 32.9610 21.4948 24 12.8443 13.1416 65 33.3110 21.9313 25 13.4001 13.2052 66 33.6479 22.3778 26 13.9554 13.2727 67 33.9717 22.8340 27 14.5103 13.3441 68 34.2819 23.2996 28 15.0646 13.4197 69 34.5783 23.7740 29 15.6182 13.4996 60 34.8608 24.2569 30 16.1713 13.5839 71 35.1291 24.7478 31 16.7236 13.6728 72 35.3830 25.2462 32 17.2751 13.7665 73 35.6224 25.7519 33 17.8257 13.8652 74 35.8470 26.2642 34 18.3754 13.9690 75 36.0569 26.7827 35 18.9241 14.0783 76 36.2519 27.3071 36 19.4715 14.1933 77 36.4318 27.8368 37 20.0178 14.3141 78 36.5966 28.3714 38 20.5626 14.4411 79 36.7463 28.9104 39 21.1059 14.5745 80 36.8808 29.4534 40 21.6474 14.7147 81 37.0000 30.0000 41 22.1871 14.8621


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Table 2: Summary of the dimensions and Kt properties of the new Modified Constant-Stress Coupon, together with those of the original design.

Original Constant-Stress Coupon

Modified Constant-Stress Coupon

Thickness (mm) 6.35 6.35 Total length (mm) 160 244 Total width (mm) 40 60 Notch length (mm) 70 74 Width of centre-section (mm) 25 25 Grip area (mm2) 40×40 = 1600 60×60 = 3600 Grip buffer zone (mm) 5 25 Arc length of notch boundary (mm) 73.9 89.5 Arc length of constant-stress zone (mm) 54.4 50.3 Net-section SCF Kt 1.038 1.048 Gross-section SCF Ktg 1.660 2.516


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Figure 1: Dimensions of a fatigue test coupon with a constant-radius notch (McDonald 2009a).

Figure 2: Tangential stress response over the notch region of a fatigue test coupon with a constant-

radius notch.

76 mm

Grip Area 40×40 mm

Grip Area 40×40 mm

160 mm

x

y

25 m

m

Notch Radius 100 mm

Notch Depth 7.5


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Figure 3: Dimensions of a fatigue test coupon with a central region of constant width and large

constant-radius fillets.

Figure 4: Tangential stress response over the notch region of a fatigue test coupon with a central

region of constant width and large constant-radius fillets.

116 mm

Grip Area 40×40 mm

200 mm

x

y

25 m

m

Fillet Radius 100 mm

Notch Depth 7.5 mm

40 mm

Grip Area 40×40 mm


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Figure 5: Dimensions of a fatigue test coupon with a central region of constant width and

moderate constant-radius fillets.

Figure 6: Tangential stress response over the notch region of a fatigue test coupon with a central

region of constant width and moderate constant-radius fillets.

79.69 mm

Grip Area 40×40 mm

Grip Area 40×40 mm

170 mm

x

y

25 m

m

Fillet Radius 30 mm

40 mm

7.5 mm


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Figure 7: General shape and dimensions of original optimised constant-stress coupon.

Figure 8: Tangential stress response over the notch region of original optimised constant-stress

coupon.

5 mm 70 mm

Grip Area 40×40 mm

Grip Area 40×40 mm

160 mm

x

y

25 mm

Buffer Zone Optimal Notch Profile

Thickness = 6.35 mm

7.5 mm


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Figure 9: General shape and dimensions of the Modified Constant-Stress Coupon.

Figure 10: Initial finite element mesh for ⅛-symmetry model of the Modified Constant-Stress

Coupon prior to shape optimisation.

25 mm 74 mm

Grip Area 60×60 mm

Grip Area 60×60 mm

244 mm

x

y

25 mm

Buffer Zone Optimal Notch Profile

25 mm

17.5 mm

Thickness = 6.35 mm


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Figure 11: Side view of 3D mesh showing the assumed starting shape of the notch and the

optimisation zone.

Figure 12: Notch profile optimal shape for the Modified Constant-Stress Coupon.

Zone of changing mesh during optimisation

Zone of fixed mesh during optimisation

Nodes fixed during optimisation


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Figure 13: Contours of maximum principal stress for the optimised constant-stress coupon.

Figure 14: Normalised maximum principal stress along optimal notch boundary for the Modified

Constant-Stress Coupon.


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Figure 15: Contours of maximum principal stress in the vicinity of constant-stress region of the

optimised Modified Constant-Stress Coupon that are within 6% of the maximum stress.

Figure 16: Contours of maximum principal stress in the vicinity of the constant-stress region of the

optimised Modified Constant-Stress Coupon that are within 1% of the maximum stress.


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Figure 17: Computed radius of curvature along the raw unsmoothed optimal boundary of the

Modified Constant-Stress Coupon.

Figure 18: Section of raw unsmoothed optimal profile showing “flat” spots and a more

representative smooth curve passing through every second point.


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Figure 19: Radius of curvature along the notch boundary after completion of manual smoothing.

Figure 20: Radius of curvature along the notch boundary after completion of an additional two

cycles of automated smoothing.


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Figure 21: Normalised maximum principal stress along smoothed optimal notch boundary for the

Modified Constant-Stress Coupon.

Figure 22: Radius of curvature along the notch boundary after completion of twenty cycles of

automated smoothing without applying any prior manual smoothing.


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Figure 23: Normalised maximum principal stress along optimal notch boundary for the Modified

Constant-Stress Coupon obtained using boundary element and finite element models.


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Figure 24: Simulated crack-growth trajectories for through-thickness edge cracks starting from

different points along the notch boundary of the Modified Constant-Stress Coupon.

Notch boundary

Crack-growth trajectory


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Figure 25: Boundary correction factors as a function of crack length for cracks starting at different

points along the notch boundary of the Modified Constant-Stress Coupon.

Figure 26: Boundary correction factors as a function of distance along the notch boundary for

cracks of varying lengths for the Modified Constant-Stress Coupon.

F = 1.1215

F = 1.1215


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Appendix A:

FADD2D input file for uncracked notch composed of large 100-mm constant-radius arcs

The following input file can also be found stored in Objective folder fAV1044714.

FADD - Visual C++ Version 1.0 - 09/10/14 Dog-bone Fatigue Test Coupon Constant R = 100 mm Radius Notch ------------------------------------------------------- Problem Type, No of Materials 2 1 Materials, Elastic modulus, and Poisson's ratio 1 72400.000000 0.330000 Material, Cracks, Boundaries, and Point loads 1 0 1 0 Input echo, Boundary Stresses, and Displacements 1 1 1 ------------------------------------------------------- Definition of Boundary 1 1 0 0 5 1 0 0.000000 112.500000 100.000000 60 -90.000000 -1 0.000000 -1 0.000000 0 -101.165823 -1 0.000000 -1 0.000000 0 -112.331645 -1 0.000000 -1 0.000000 0 2 1 30 -37.996710 20.000000 -1 0.000000 -1 0.000000 0 -58.998355 20.000000 -1 0.000000 -1 0.000000 0 -80.000000 20.000000 -1 0.000000 -1 0.000000 0 3 1 30 -80.000000 20.000000 -1 -100.000000 -1 0.000000 0 -80.000000 10.000000 -1 -100.000000 -1 0.000000 0 -80.000000 0.000000 -1 -100.000000 -1 0.000000 0 4 1 40 -80.000000 0.000000 -1 0.000000 0 0.000000 0 -40.000000 0.000000 -1 0.000000 0 0.000000 0 0.000000 0.000000 -1 0.000000 0 0.000000 0 5 1 40 0.000000 0.000000 0 0.000000 -1 0.000000 0 0.000000 6.250000 0 0.000000 -1 0.000000 0 0.000000 12.500000 0 0.000000 -1 0.000000 0 -------------------------------------------------------


UNCLASSIFIED 36

Appendix B:

FADD2D input file for uncracked notch with constant central width and large 100-mm radius fillets


FADD - Visual C++ Version 1.0 - 09/10/14 Dog-bone Fatigue Test Coupon 40 mm Uniform Section With R = 100 mm Radius Fillets ------------------------------------------------------- Problem Type, No of Materials 2 1 Materials, Elastic modulus, and Poisson's ratio 1 72400.000000 0.330000 Material, Cracks, Boundaries, and Point loads 1 0 1 0 Input echo, Boundary Stresses, and Displacements 1 1 1 ------------------------------------------------------- Definition of Boundary 1 1 0 0 6 1 1 30 0.000000 12.500000 -1 0.000000 -1 0.000000 0 -10.000000 12.500000 -1 0.000000 -1 0.000000 0 -20.000000 12.500000 -1 0.000000 -1 0.000000 0 2 0 -20.000000 112.500000 100.000000 60 -90.000000 -1 0.000000 -1 0.000000 0 -101.165823 -1 0.000000 -1 0.000000 0 -112.331645 -1 0.000000 -1 0.000000 0 3 1 30 -57.996710 20.000000 -1 0.000000 -1 0.000000 0 -78.998355 20.000000 -1 0.000000 -1 0.000000 0 -100.000000 20.000000 -1 0.000000 -1 0.000000 0 4 1 30 -100.000000 20.000000 -1 -100.000000 -1 0.000000 0 -100.000000 10.000000 -1 -100.000000 -1 0.000000 0 -100.000000 0.000000 -1 -100.000000 -1 0.000000 0 5 1 40 -100.000000 0.000000 -1 0.000000 0 0.000000 0 -50.000000 0.000000 -1 0.000000 0 0.000000 0 0.000000 0.000000 -1 0.000000 0 0.000000 0 6 1 40 0.000000 0.000000 0 0.000000 -1 0.000000 0


UNCLASSIFIED 37

0.000000 6.250000 0 0.000000 -1 0.000000 0 0.000000 12.500000 0 0.000000 -1 0.000000 0 -------------------------------------------------------


UNCLASSIFIED 38

Appendix C:

FADD2D input file for uncracked notch with constant central width and medium 30-mm radius fillets


FADD - Visual C++ Version 1.0 - 09/10/14 Dog-bone Fatigue Test Coupon 40 mm Uniform Section With R = 100 mm Radius Fillets ------------------------------------------------------- Problem Type, No of Materials 2 1 Materials, Elastic modulus, and Poisson's ratio 1 72400.000000 0.330000 Material, Cracks, Boundaries, and Point loads 1 0 1 0 Input echo, Boundary Stresses, and Displacements 1 1 1 1 ------------------------------------------------------- Definition of Boundary 1 1 0 0 6 1 1 30 0.000000 12.500000 -1 0.000000 -1 0.000000 0 -10.000000 12.500000 -1 0.000000 -1 0.000000 0 -20.000000 12.500000 -1 0.000000 -1 0.000000 0 2 0 -20.000000 42.500000 30.000000 60 -90.000000 -1 0.000000 -1 0.000000 0 -110.704811 -1 0.000000 -1 0.000000 0 -131.409622 -1 0.000000 -1 0.000000 0 3 1 30 -39.843134 20.000000 -1 0.000000 -1 0.000000 0 -62.421567 20.000000 -1 0.000000 -1 0.000000 0 -85.000000 20.000000 -1 0.000000 -1 0.000000 0 4 1 30 -85.000000 20.000000 -1 -100.000000 -1 0.000000 0 -85.000000 10.000000 -1 -100.000000 -1 0.000000 0 -85.000000 0.000000 -1 -100.000000 -1 0.000000 0 5 1 40 -85.000000 0.000000 -1 0.000000 0 0.000000 0 -42.500000 0.000000 -1 0.000000 0 0.000000 0 0.000000 0.000000 -1 0.000000 0 0.000000 0 6 1 40 0.000000 0.000000 0 0.000000 -1 0.000000 0


UNCLASSIFIED 39

0.000000 6.250000 0 0.000000 -1 0.000000 0 0.000000 12.500000 0 0.000000 -1 0.000000 0 -------------------------------------------------------


UNCLASSIFIED 40

Appendix D:

Fortran 90 source code for the CreateDogboneCouponModel program

The following source code can also be found stored in Objective folder fAV1044714.

!============================================================================= ! ! PROGRAM: CreateDogboneCouponModel ! ! PURPOSE: To take a set of points that define the curved boundary and outer ! geometry of a dog-bone specimen and create a FADD2D model. Two ! models are created, one with and the other without an edge crack. ! ! AUTHOR: Witold Waldman ! ! DATE: 2014-08-04 ! !============================================================================ program CreateDogboneCouponModel call DogboneCouponModel(.TRUE.) call DogboneCouponModel(.FALSE.) end program CreateDogboneCouponModel !============================================================================ subroutine DogboneCouponModel(cracked) ! ! |#------------------------ l ----------------------------#| ! ! B03 B02 B01 B14 B13 B12 ! <--- +-------Y--------+ +--------Y-------+ ---> ---- ! <--- | \ /Cn | ---> # ! <--- | \________+________/ | ---> | ! <--- | C1 | ---> | ! <--- | | ---> | ! <--- XY B04 + (x,y) origin B11 Y ---> h ! <--- | | ---> | ! <--- | ________+_______ | ---> | ! <--- | / \ | ---> | ! <--- | / \ | ---> # ! <--- +-------Y--------+ +--------Y-------+ ---> ---- ! B05 B06 B07 B08 B09 B10 ! implicit none integer(4), parameter :: lui = 1


UNCLASSIFIED 41

integer(4), parameter :: luo = 2 integer(4), parameter :: nb = 14 integer(4), parameter :: ndash = 86 integer(4), parameter :: maxpts = 1000 real(8) , parameter :: px = 100.0d0 logical(4) cracked character str(100)*128,filedbi*32,filedbc*32,filedbu*32 integer(4) nc,ncracks,nelemcrack real(8) cx(maxpts),cy(maxpts) real(8) bx(nb),by(nb) integer(4) id,ic,i,j,nelem integer(4) icrackpoint(maxpts) real(8) ls,lg,hon2,lon2,dx,dy,a0,da,plexp real(8) ym,nu complex(8) z1,z2,z3 integer(4) cn(maxpts) real(8) angletangent(maxpts),anglenormal(maxpts) real(8) xinwnv(maxpts),yinwnv(maxpts) real(8) cangletangent(maxpts),canglenormal(maxpts) real(8) cxinwnv(maxpts),cyinwnv(maxpts) integer(4) nsteps filedbi = 'dogbone.dat' filedbc = 'dogbone_cracked.in' filedbu = 'dogbone_uncracked.in' do i = 1,maxpts icrackpoint(i) = 0 enddo open(lui,file=filedbi,status='OLD') read(lui,*) ym,nu read(lui,*) ls,lg read(lui,*) ncracks,a0,nsteps,da,plexp,(icrackpoint(i),i=1,ncracks) read(lui,*) nc do i = 1,nc read(lui,*) cx(i),cy(i) end do close(lui) if (cracked) then if (ncracks.le.0) then write(*,*) 'No cracks were defined. Proceeding to place a crack' write(*,*) 'at the first node on the line of symmetry.' ncracks = 1 icrackpoint(1) = 1 endif open(unit=luo,file=filedbc,status='REPLACE') else ncracks = 0 do i = 1,maxpts icrackpoint(i) = 0 enddo open(unit=luo,file=filedbu,status='REPLACE')


UNCLASSIFIED 42

endif hon2 = cy(nc) lon2 = ls/2.0d0 bx(01) = -cx(nc); by(01) = +hon2 bx(02) = -lon2+lg; by(02) = +hon2 bx(03) = -lon2; by(03) = +hon2 bx(04) = -lon2; by(04) = 0.0d0 bx(05) = -lon2; by(05) = -hon2 bx(06) = -lon2+lg; by(06) = -hon2 bx(07) = -cx(nc); by(07) = -hon2 bx(08) = +cx(nc); by(08) = -hon2 bx(09) = +lon2-lg; by(09) = -hon2 bx(10) = +lon2; by(10) = -hon2 bx(11) = +lon2; by(11) = 0.0d0 bx(12) = +lon2; by(12) = +hon2 bx(13) = +lon2-lg; by(13) = +hon2 bx(14) = +cx(nc); by(14) = +hon2 do i = 1,nc cn(i) = 0 enddo do i = 1,ncracks cn(icrackpoint(i)) = i enddo call anglevector(nc,cx,cy,angletangent,anglenormal,xinwnv,yinwnv) write(luo,'(a)') 'FADD2D input deck generated by CreateDogboneCouponModel' write(luo,'(a)') 'Dogbone Fatigue Analysis Coupon' if (cracked) then write(luo,'(a)') 'Edge cracked case' else write(luo,'(a)') 'Uncracked case' endif call writedashedline(luo,ndash) write(luo,'(a)') 'Problem Type, No of Materials' write(luo,'(a)') '2 1' write(luo,'(a)') 'Materials, Elastic modulus, and Poisson''s ratio' write(luo,'(i1,f20.4,f17.4)') 1,ym,nu write(luo,'(a)') 'Material, Cracks, Boundaries, and Point loads' if (cracked) then write(luo,'(i1,i5.4,2i2)') 1,ncracks,1,0 write(luo,'(a)') 'Crack-growth steps, increment, and Paris law exponent' write(luo,'(i4.4,2f12.4)') nsteps,da,plexp else write(luo,'(a)') '1 0 1 0' endif write(luo,'(a)') 'Input echo, Boundary Stresses, and Displacements' write(luo,'(a)') '1 1 1 1'


UNCLASSIFIED 43

write(luo,'(a)') '' if (cracked) then call writedashedline(luo,ndash) write(luo,'(a)') 'Definition of Crack' write(luo,'(a)') '' nelemcrack = 8 do i = 1,ncracks write(luo,'(i4.4,i2)') i,1 write(luo,'(a)') ' 1 0 0 2 1' j = icrackpoint(i) if (mod(j,2) .eq. 0) then write(*,*) write(*,*) 'Error: Crack location index must be an odd number. Check your input data.' write(*,*) stop endif dx = a0*xinwnv(j) dy = a0*yinwnv(j) write(luo,'(2i4,4f18.7,i6,f18.3)') 1,1,cx(j),cy(j),cx(j)+dx,cy(j)+dy,nelemcrack,anglenormal(j) write(luo,'(a)') '' enddo endif call writedashedline(luo,ndash) write(luo,'(a)') 'Definition of Boundary' write(luo,'(a)') '' write(luo,'(a)') '1 1' write(luo,'(i4.4,i2,i6)') ncracks,0,4*(nc/2)+nb-2 ! Initialise counter that gets incremented when each ! boundary segment is created. id = 0 ! Write out the LH upper quadrant of the curved boundary. nelem = 2 do i = 1,nc/2 ic = (i-1)*2+1 if (i.eq.1 .and. cn(1).gt.0) then call segpara(-cx(ic),+cy(ic),-cx(ic+1),+cy(ic+1),-cx(ic+2),+cy(ic+2), & cn(ic),0,0,luo,id,8*nelem) else call segpara(-cx(ic),+cy(ic),-cx(ic+1),+cy(ic+1),-cx(ic+2),+cy(ic+2), & 0,0,0,luo,id,nelem) endif enddo ! Write out next line segments. nelem = 4 call segline(bx(01),by(01),bx(02),by(02),luo,id,nelem,-1,0.0d0,-1,0.0d0,3,0,1) call segline(bx(02),by(02),bx(03),by(03),luo,id,nelem,-1,0.0d0,-1,0.0d0,1,0,1)


UNCLASSIFIED 44

call segline(bx(03),by(03),bx(04),by(04),luo,id,nelem,-1, -px ,-1,0.0d0,3,1,1) call segline(bx(04),by(04),bx(05),by(05),luo,id,nelem,-1, -px ,-1,0.0d0,1,1,1) call segline(bx(05),by(05),bx(06),by(06),luo,id,nelem,-1,0.0d0,-1,0.0d0,3,0,1) call segline(bx(06),by(06),bx(07),by(07),luo,id,nelem,-1,0.0d0,-1,0.0d0,1,0,1) ! Write out the LH lower quadrant of the curved boundary. nelem = 1 do i = 1,nc/2 ic = nc-(i-1)*2 call segpara(-cx(ic),-cy(ic),-cx(ic-1),-cy(ic-1),-cx(ic-2),-cy(ic-2), & 0,0,0,luo,id,nelem) enddo ! Write out the RH lower quadrant of the curved boundary. nelem = 1 do i = 1,nc/2 ic = (i-1)*2+1 call segpara(+cx(ic),-cy(ic),+cx(ic+1),-cy(ic+1),+cx(ic+2),-cy(ic+2), & 0,0,0,luo,id,nelem) enddo ! Write out next line segments. nelem = 4 call segline(bx(08),by(08),bx(09),by(09),luo,id,nelem,-1,0.0d0,-1,0.0d0,3,0,1) call segline(bx(09),by(09),bx(10),by(10),luo,id,nelem,-1,0.0d0,-1,0.0d0,1,0,1) call segline(bx(10),by(10),bx(11),by(11),luo,id,nelem,-1, +px ,-1,0.0d0,3,0,1) call segline(bx(11),by(11),bx(12),by(12),luo,id,nelem,-1, +px ,-1,0.0d0,1,0,1) call segline(bx(12),by(12),bx(13),by(13),luo,id,nelem,-1,0.0d0,-1,0.0d0,3,0,1) call segline(bx(13),by(13),bx(14),by(14),luo,id,nelem,-1,0.0d0,-1,0.0d0,1,0,1) ! Write out the RH upper quadrant of the curved boundary. nelem = 2 do i = 1,nc/2 ic = nc-(i-1)*2 ! If a crack is located at either the start or end node of the ! parabolic segment, increase the mesh density for the segment. if (cn(ic).gt.0 .or. cn(ic-2).gt.0) then call segpara(+cx(ic),+cy(ic),+cx(ic-1),+cy(ic-1),+cx(ic-2),+cy(ic-2), & cn(ic),cn(ic-1),cn(ic-2),luo,id,8*nelem) else call segpara(+cx(ic),+cy(ic),+cx(ic-1),+cy(ic-1),+cx(ic-2),+cy(ic-2), & cn(ic),cn(ic-1),cn(ic-2),luo,id,nelem) endif enddo write(luo,'(a)') ' ' call writedashedline(luo,ndash) close(luo) end subroutine DogboneCouponModel


UNCLASSIFIED 45

!============================================================================= subroutine writedashedline(luo,ndash) implicit none integer(4) luo,ndash,i write(luo,'(2000a)') ('-',i=1,ndash) end subroutine writedashedline !============================================================================= subroutine segpara(x1,y1,x2,y2,x3,y3,cn1,cn2,cn3,luo,id,nelem) implicit none real(8) x1,y1,x2,y2,x3,y3 integer(4) cn1,cn2,cn3 integer(4) luo,id,nelem id = id + 1 write(luo,'(a)') '' write(luo,'(i4.4,2i4)') id,1,nelem write(luo,'(2f15.7,i4,f15.7,i4,f15.7,i4)') x1,y1,-1,0.0d0,-1,0.0d0,cn1 write(luo,'(2f15.7,i4,f15.7,i4,f15.7,i4)') x2,y2,-1,0.0d0,-1,0.0d0,cn2 write(luo,'(2f15.7,i4,f15.7,i4,f15.7,i4)') x3,y3,-1,0.0d0,-1,0.0d0,cn3 return end subroutine segpara !============================================================================= subroutine segline(x1,y1,x2,y2,luo,id,nelem,icx,vcx,icy,vcy,icn,icnx,icny) implicit none real(8) x1,y1,x2,y2,vcx,vcy integer(4) luo,id,nelem,icx,icy,icn,icnx,icny real(8) px real(8) xm,ym id = id + 1 xm = (x1+x2)/2.0d0 ym = (y1+y2)/2.0d0 write(luo,'(a)') '' write(luo,'(i4.4,2i4)') id,1,nelem if (icn.eq.0) then write(luo,100) x1,y1,icx,vcx,icy,vcy,0 write(luo,100) xm,ym,icx,vcx,icy,vcy,0 write(luo,100) x2,y2,icx,vcx,icy,vcy,0


UNCLASSIFIED 46

else if (icn.eq.1) then write(luo,100) x1,y1,icx,vcx,icy,vcy,-2,icnx,icny else write(luo,100) x1,y1,icx,vcx,icy,vcy,0 end if if (icn.eq.2) then write(luo,100) xm,ym,icx,vcx,icy,vcy,-2,icnx,icny else write(luo,100) xm,ym,icx,vcx,icy,vcy,0 end if if (icn.eq.3) then write(luo,100) x2,y2,icx,vcx,icy,vcy,-2,icnx,icny else write(luo,100) x2,y2,icx,vcx,icy,vcy,0 end if end if return 100 format(2f15.7,i4,f15.7,i4,f15.7,3i4) end subroutine segline !============================================================================= subroutine anglevector(n,xc,yc,angletangent,anglenormal,xinwnv,yinwnv) ! Determine the tangent angle, inward normal angle, and inward normal vector ! for points along the curved optimal boundary. It is assumed that the first ! point is mirrored about the y-axis. implicit none integer(4) n real(8) xc(n),yc(n),angletangent(n),anglenormal(n),xinwnv(n),yinwnv(n) integer(4) i real(8) pi,pion2,twopi pi = 4.0d0*atan(1.0d0) pion2 = pi/2.0d0 twopi = 2.0d0*pi do i=1,n ! Compute angle of slope of the curve at each point on the curve. if (i.eq.1) then angletangent(i)=atan2(0.0d0,xc(i+1)-(-xc(i+1))) else if (i.eq.n) then angletangent(i)=atan2(yc(i)-yc(i-1),xc(i)-xc(i-1)) else ! This simple formula for calculating the slope of the ! curve is equivalent to what is obtained by using ! a second-order Lagrange polynomial approximation. angletangent(i)=atan2(yc(i+1)-yc(i-1),xc(i+1)-xc(i-1)) endif ! Compute angle of the outward normal.


UNCLASSIFIED 47

anglenormal(i)=angletangent(i)-pion2 if (anglenormal(i).gt.pi) anglenormal(i)=anglenormal(i)-twopi ! Compute inward unit normal vector to boundary. xinwnv(i)=cos(anglenormal(i)) yinwnv(i)=sin(anglenormal(i)) ! Convert angles from radians to degrees. anglenormal(i)=anglenormal(i)*180.0d0/pi angletangent(i)=angletangent(i)*180.0d0/pi enddo return end !============================================================================= subroutine circle(x1,y1,x2,y2,x3,y3,xc,yc,r,det) ! Determine the centre coordinates (xc,yc) and radius r of a circle passing ! through three points, (x1,y1) (x2,y2) (x3,y3). ! ! If the value of det is zero, then a circle through the three given points ! does not exist. e.g. the three points are colinear. implicit none real*8 x1,y1,x2,y2,x3,y3,xc,yc,r,det real*8 a1,a2,c1,c2,b1,b2 a1=2.0*(x2-x1) a2=2.0*(x3-x2) b1=2.0*(y2-y1) b2=2.0*(y3-y2) c1=x2**2+y2**2-x1**2-y1**2 c2=x3**2+y3**2-x2**2-y2**2 det=a1*b2-b1*a2 if (det.ne.0.0) then xc=(c1*b2-b1*c2)/det yc=(a1*c2-c1*a2)/det a1=xc-x1 a2=yc-y1 r=dsqrt(a1**2+a2**2) else xc=0.0d0 yc=0.0d0 r=0.0d0 endif return end !============================================================================= subroutine canglevector(n,xc,yc,angletangent,anglenormal,xinwnv,yinwnv)


UNCLASSIFIED 48

! Determine the tangent angle, inward normal angle, and inward normal vector ! for points along the curved optimal boundary. It is assumed that the first ! point is mirrored about the y-axis. implicit none integer(4) n real(8) xc(n),yc(n),angletangent(n),anglenormal(n),xinwnv(n),yinwnv(n) integer(4) i real(8) pi,pion2,twopi,r,cx,cy,det pi = 4.0d0*atan(1.0d0) pion2 = pi/2.0d0 twopi = 2.0d0*pi do i=1,n ! Compute angle of slope of the curve at each point on the curve. if (i.eq.1) then call circle(-xc(i+1),yc(i+1),xc(i),yc(i),xc(i+1),yc(i+1),cx,cy,r,det) if (det.eq.0.0d0) then angletangent(i)=atan2(0.0d0,xc(i+1)-(-xc(i+1))) endif else if (i.eq.n) then call circle(xc(i-2),yc(i-2),xc(i-1),yc(i-1),xc(i),yc(i),cx,cy,r,det) if (det.eq.0.0d0) then angletangent(i)=atan2(yc(i)-yc(i-1),xc(i)-xc(i-1)) endif else call circle(xc(i-1),yc(i-1),xc(i),yc(i),xc(i+1),yc(i+1),cx,cy,r,det) if (det.eq.0.0d0) then angletangent(i)=atan2(yc(i+1)-yc(i-1),xc(i+1)-xc(i-1)) endif endif ! Compute angle of the outward normal. if (det.eq.0.0d0) then anglenormal(i)=angletangent(i)-pion2 else anglenormal(i) = atan2(yc(i)-cy,xc(i)-cx) angletangent(i) = anglenormal(i)+pion2 endif if (anglenormal(i).gt.pi) anglenormal(i)=anglenormal(i)-twopi ! Compute inward unit normal vector to boundary. xinwnv(i)=cos(anglenormal(i)) yinwnv(i)=sin(anglenormal(i)) ! Convert angles from radians to degrees. anglenormal(i)=anglenormal(i)*180.0d0/pi angletangent(i)=angletangent(i)*180.0d0/pi enddo return end


UNCLASSIFIED 49

Appendix E:

Input deck used to create FADD2D model of original constant-stress coupon using

CreateDogboneCouponModel program


72400.0 0.33 160.0 40.0 1 0.10 199 0.10 3.0 1 37 0.000000 12.500000 1.040013 12.502718 2.096924 12.510549 3.153789 12.523134 4.210584 12.540315 5.267295 12.562121 6.323909 12.588742 7.380377 12.620489 8.436671 12.657774 9.492742 12.700915 10.548531 12.750359 11.603993 12.806458 12.659052 12.869623 13.713637 12.940341 14.767647 13.019109 15.820983 13.106494 16.873507 13.203122 17.925085 13.309665 18.975613 13.426894 20.024801 13.555622 21.072376 13.696856 22.118006 13.851865 23.161242 14.022339 24.201506 14.210653 25.237661 14.420102 26.268244 14.655024 27.290857 14.921516 28.302109 15.226401 29.297739 15.579076 30.271200 15.988238 31.212088 16.463631 32.102810 17.007961 32.937607 17.631344 33.710354 18.341629 34.400757 19.132950 34.700379 19.566475 35.000000 20.000000


UNCLASSIFIED 50

Appendix F:

FADD2D input file for Modified Constant-Stress Coupon with one centrally-located through-thickness

edge crack


FADD2D input deck generated by CreateDogboneCouponModel Dog-bone Fatigue Analysis Coupon Edge cracked case -------------------------------------------------------------------------------------- Problem Type, No of Materials 2 1 Materials, Elastic modulus, and Poisson's ratio 1 72400.0000 0.3000 Material, Cracks, Boundaries, and Point loads 1 0001 1 0 Crack-growth steps, increment, and Paris law exponent 0199 0.1000 3.0000 Input echo, Boundary Stresses, and Displacements 1 1 1 1 -------------------------------------------------------------------------------------- Definition of Crack 0001 1 1 0 0 2 1 1 1 0.0000000 12.5000000 0.0000000 12.4000000 8 -90.000 -------------------------------------------------------------------------------------- Definition of Boundary 1 1 0001 0 172 0001 1 16 0.0000000 12.5000000 -1 0.0000000 -1 0.0000000 1 -0.5269560 12.5009750 -1 0.0000000 -1 0.0000000 0 -1.0548970 12.5038980 -1 0.0000000 -1 0.0000000 0 0002 1 2 -1.0548970 12.5038980 -1 0.0000000 -1 0.0000000 0 -1.5831520 12.5087610 -1 0.0000000 -1 0.0000000 0 -2.1121110 12.5155840 -1 0.0000000 -1 0.0000000 0 0003 1 2 -2.1121110 12.5155840 -1 0.0000000 -1 0.0000000 0 -2.6419170 12.5243890 -1 0.0000000 -1 0.0000000 0 -3.1729650 12.5352090 -1 0.0000000 -1 0.0000000 0 0004 1 2 -3.1729650 12.5352090 -1 0.0000000 -1 0.0000000 0 -3.7053990 12.5481030 -1 0.0000000 -1 0.0000000 0 -4.2397240 12.5631460 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 51

0005 1 2 -4.2397240 12.5631460 -1 0.0000000 -1 0.0000000 0 -4.7759650 12.5803830 -1 0.0000000 -1 0.0000000 0 -5.3146670 12.5998890 -1 0.0000000 -1 0.0000000 0 0006 1 2 -5.3146670 12.5998890 -1 0.0000000 -1 0.0000000 0 -5.8545820 12.6217180 -1 0.0000000 -1 0.0000000 0 -6.3876870 12.6455960 -1 0.0000000 -1 0.0000000 0 0007 1 2 -6.3876870 12.6455960 -1 0.0000000 -1 0.0000000 0 -6.9200650 12.6717650 -1 0.0000000 -1 0.0000000 0 -7.4515850 12.7002270 -1 0.0000000 -1 0.0000000 0 0008 1 2 -7.4515850 12.7002270 -1 0.0000000 -1 0.0000000 0 -7.9827010 12.7310960 -1 0.0000000 -1 0.0000000 0 -8.5133160 12.7644570 -1 0.0000000 -1 0.0000000 0 0009 1 2 -8.5133160 12.7644570 -1 0.0000000 -1 0.0000000 0 -9.0435910 12.8003850 -1 0.0000000 -1 0.0000000 0 -9.5734790 12.8389350 -1 0.0000000 -1 0.0000000 0 0010 1 2 -9.5734790 12.8389350 -1 0.0000000 -1 0.0000000 0 -10.1029990 12.8802070 -1 0.0000000 -1 0.0000000 0 -10.6321650 12.9243020 -1 0.0000000 -1 0.0000000 0 0011 1 2 -10.6321650 12.9243020 -1 0.0000000 -1 0.0000000 0 -11.1609440 12.9712940 -1 0.0000000 -1 0.0000000 0 -11.6893620 13.0212660 -1 0.0000000 -1 0.0000000 0 0012 1 2 -11.6893620 13.0212660 -1 0.0000000 -1 0.0000000 0 -12.2173350 13.0743260 -1 0.0000000 -1 0.0000000 0 -12.7449000 13.1306100 -1 0.0000000 -1 0.0000000 0 0013 1 2 -12.7449000 13.1306100 -1 0.0000000 -1 0.0000000 0 -13.2720240 13.1902110 -1 0.0000000 -1 0.0000000 0 -13.7986800 13.2532360 -1 0.0000000 -1 0.0000000 0 0014 1 2 -13.7986800 13.2532360 -1 0.0000000 -1 0.0000000 0 -14.3248320 13.3197950 -1 0.0000000 -1 0.0000000 0 -14.8504690 13.3900040 -1 0.0000000 -1 0.0000000 0 0015 1 2 -14.8504690 13.3900040 -1 0.0000000 -1 0.0000000 0 -15.3755720 13.4640060 -1 0.0000000 -1 0.0000000 0 -15.9001150 13.5419440 -1 0.0000000 -1 0.0000000 0 0016 1 2 -15.9001150 13.5419440 -1 0.0000000 -1 0.0000000 0 -16.4240060 13.6239530 -1 0.0000000 -1 0.0000000 0 -16.9472920 13.7101910 -1 0.0000000 -1 0.0000000 0 0017 1 2 -16.9472920 13.7101910 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 52

-17.4698810 13.8008030 -1 0.0000000 -1 0.0000000 0 -17.9918290 13.8959670 -1 0.0000000 -1 0.0000000 0 0018 1 2 -17.9918290 13.8959670 -1 0.0000000 -1 0.0000000 0 -18.5130540 13.9958890 -1 0.0000000 -1 0.0000000 0 -19.0334590 14.1008050 -1 0.0000000 -1 0.0000000 0 0019 1 2 -19.0334590 14.1008050 -1 0.0000000 -1 0.0000000 0 -19.5530890 14.2109080 -1 0.0000000 -1 0.0000000 0 -20.0719290 14.3264120 -1 0.0000000 -1 0.0000000 0 0020 1 2 -20.0719290 14.3264120 -1 0.0000000 -1 0.0000000 0 -20.5900300 14.4476180 -1 0.0000000 -1 0.0000000 0 -21.1072320 14.5748160 -1 0.0000000 -1 0.0000000 0 0021 1 2 -21.1072320 14.5748160 -1 0.0000000 -1 0.0000000 0 -21.6237560 14.7084000 -1 0.0000000 -1 0.0000000 0 -22.1392270 14.8486600 -1 0.0000000 -1 0.0000000 0 0022 1 2 -22.1392270 14.8486600 -1 0.0000000 -1 0.0000000 0 -22.6541940 14.9961780 -1 0.0000000 -1 0.0000000 0 -23.1680960 15.1513480 -1 0.0000000 -1 0.0000000 0 0023 1 2 -23.1680960 15.1513480 -1 0.0000000 -1 0.0000000 0 -23.6814600 15.3152570 -1 0.0000000 -1 0.0000000 0 -24.1937660 15.4889750 -1 0.0000000 -1 0.0000000 0 0024 1 2 -24.1937660 15.4889750 -1 0.0000000 -1 0.0000000 0 -24.7067210 15.6738580 -1 0.0000000 -1 0.0000000 0 -25.2644210 15.8886490 -1 0.0000000 -1 0.0000000 0 0025 1 2 -25.2644210 15.8886490 -1 0.0000000 -1 0.0000000 0 -25.8168760 16.1193410 -1 0.0000000 -1 0.0000000 0 -26.3618170 16.3672470 -1 0.0000000 -1 0.0000000 0 0026 1 2 -26.3618170 16.3672470 -1 0.0000000 -1 0.0000000 0 -26.8985910 16.6322690 -1 0.0000000 -1 0.0000000 0 -27.4269430 16.9135610 -1 0.0000000 -1 0.0000000 0 0027 1 2 -27.4269430 16.9135610 -1 0.0000000 -1 0.0000000 0 -27.9463980 17.2108080 -1 0.0000000 -1 0.0000000 0 -28.4564090 17.5238130 -1 0.0000000 -1 0.0000000 0 0028 1 2 -28.4564090 17.5238130 -1 0.0000000 -1 0.0000000 0 -28.9564640 17.8523280 -1 0.0000000 -1 0.0000000 0 -29.4460510 18.1960790 -1 0.0000000 -1 0.0000000 0 0029 1 2 -29.4460510 18.1960790 -1 0.0000000 -1 0.0000000 0 -29.9246720 18.5547780 -1 0.0000000 -1 0.0000000 0 -30.3918430 18.9281140 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 53

0030 1 2 -30.3918430 18.9281140 -1 0.0000000 -1 0.0000000 0 -30.8470810 19.3157570 -1 0.0000000 -1 0.0000000 0 -31.2899290 19.7173620 -1 0.0000000 -1 0.0000000 0 0031 1 2 -31.2899290 19.7173620 -1 0.0000000 -1 0.0000000 0 -31.7199390 20.1325620 -1 0.0000000 -1 0.0000000 0 -32.1366780 20.5609680 -1 0.0000000 -1 0.0000000 0 0032 1 2 -32.1366780 20.5609680 -1 0.0000000 -1 0.0000000 0 -32.5397330 21.0021790 -1 0.0000000 -1 0.0000000 0 -32.9287130 21.4557740 -1 0.0000000 -1 0.0000000 0 0033 1 2 -32.9287130 21.4557740 -1 0.0000000 -1 0.0000000 0 -33.3032360 21.9213120 -1 0.0000000 -1 0.0000000 0 -33.6629540 22.3983410 -1 0.0000000 -1 0.0000000 0 0034 1 2 -33.6629540 22.3983410 -1 0.0000000 -1 0.0000000 0 -34.0075320 22.8863920 -1 0.0000000 -1 0.0000000 0 -34.3366610 23.3849790 -1 0.0000000 -1 0.0000000 0 0035 1 2 -34.3366610 23.3849790 -1 0.0000000 -1 0.0000000 0 -34.6500560 23.8936100 -1 0.0000000 -1 0.0000000 0 -34.9474520 24.4117710 -1 0.0000000 -1 0.0000000 0 0036 1 2 -34.9474520 24.4117710 -1 0.0000000 -1 0.0000000 0 -35.2286050 24.9389450 -1 0.0000000 -1 0.0000000 0 -35.4933050 25.4746060 -1 0.0000000 -1 0.0000000 0 0037 1 2 -35.4933050 25.4746060 -1 0.0000000 -1 0.0000000 0 -35.7413540 26.0182160 -1 0.0000000 -1 0.0000000 0 -35.9725840 26.5692330 -1 0.0000000 -1 0.0000000 0 0038 1 2 -35.9725840 26.5692330 -1 0.0000000 -1 0.0000000 0 -36.1868470 27.1271100 -1 0.0000000 -1 0.0000000 0 -36.3840200 27.6912950 -1 0.0000000 -1 0.0000000 0 0039 1 2 -36.3840200 27.6912950 -1 0.0000000 -1 0.0000000 0 -36.5639950 28.2612320 -1 0.0000000 -1 0.0000000 0 -36.7266910 28.8363660 -1 0.0000000 -1 0.0000000 0 0040 1 2 -36.7266910 28.8363660 -1 0.0000000 -1 0.0000000 0 -36.8720530 29.4161390 -1 0.0000000 -1 0.0000000 0 -37.0000000 30.0000000 -1 0.0000000 -1 0.0000000 0 0041 1 4 -37.0000000 30.0000000 -1 0.0000000 -1 0.0000000 0 -49.5000000 30.0000000 -1 0.0000000 -1 0.0000000 0 -62.0000000 30.0000000 -1 0.0000000 -1 0.0000000 -2 0 1 0042 1 4


UNCLASSIFIED 54

-62.0000000 30.0000000 -1 0.0000000 -1 0.0000000 -2 0 1 -92.0000000 30.0000000 -1 0.0000000 -1 0.0000000 0 -122.0000000 30.0000000 -1 0.0000000 -1 0.0000000 0 0043 1 4 -122.0000000 30.0000000 -1 -100.0000000 -1 0.0000000 0 -122.0000000 15.0000000 -1 -100.0000000 -1 0.0000000 0 -122.0000000 0.0000000 -1 -100.0000000 -1 0.0000000 -2 1 1 0044 1 4 -122.0000000 0.0000000 -1 -100.0000000 -1 0.0000000 -2 1 1 -122.0000000 -15.0000000 -1 -100.0000000 -1 0.0000000 0 -122.0000000 -30.0000000 -1 -100.0000000 -1 0.0000000 0 0045 1 4 -122.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 -92.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 -62.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 -2 0 1 0046 1 4 -62.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 -2 0 1 -49.5000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 -37.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 0047 1 1 -37.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 -36.8720530 -29.4161390 -1 0.0000000 -1 0.0000000 0 -36.7266910 -28.8363660 -1 0.0000000 -1 0.0000000 0 0048 1 1 -36.7266910 -28.8363660 -1 0.0000000 -1 0.0000000 0 -36.5639950 -28.2612320 -1 0.0000000 -1 0.0000000 0 -36.3840200 -27.6912950 -1 0.0000000 -1 0.0000000 0 0049 1 1 -36.3840200 -27.6912950 -1 0.0000000 -1 0.0000000 0 -36.1868470 -27.1271100 -1 0.0000000 -1 0.0000000 0 -35.9725840 -26.5692330 -1 0.0000000 -1 0.0000000 0 0050 1 1 -35.9725840 -26.5692330 -1 0.0000000 -1 0.0000000 0 -35.7413540 -26.0182160 -1 0.0000000 -1 0.0000000 0 -35.4933050 -25.4746060 -1 0.0000000 -1 0.0000000 0 0051 1 1 -35.4933050 -25.4746060 -1 0.0000000 -1 0.0000000 0 -35.2286050 -24.9389450 -1 0.0000000 -1 0.0000000 0 -34.9474520 -24.4117710 -1 0.0000000 -1 0.0000000 0 0052 1 1 -34.9474520 -24.4117710 -1 0.0000000 -1 0.0000000 0 -34.6500560 -23.8936100 -1 0.0000000 -1 0.0000000 0 -34.3366610 -23.3849790 -1 0.0000000 -1 0.0000000 0 0053 1 1 -34.3366610 -23.3849790 -1 0.0000000 -1 0.0000000 0 -34.0075320 -22.8863920 -1 0.0000000 -1 0.0000000 0 -33.6629540 -22.3983410 -1 0.0000000 -1 0.0000000 0 0054 1 1 -33.6629540 -22.3983410 -1 0.0000000 -1 0.0000000 0 -33.3032360 -21.9213120 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 55

-32.9287130 -21.4557740 -1 0.0000000 -1 0.0000000 0 0055 1 1 -32.9287130 -21.4557740 -1 0.0000000 -1 0.0000000 0 -32.5397330 -21.0021790 -1 0.0000000 -1 0.0000000 0 -32.1366780 -20.5609680 -1 0.0000000 -1 0.0000000 0 0056 1 1 -32.1366780 -20.5609680 -1 0.0000000 -1 0.0000000 0 -31.7199390 -20.1325620 -1 0.0000000 -1 0.0000000 0 -31.2899290 -19.7173620 -1 0.0000000 -1 0.0000000 0 0057 1 1 -31.2899290 -19.7173620 -1 0.0000000 -1 0.0000000 0 -30.8470810 -19.3157570 -1 0.0000000 -1 0.0000000 0 -30.3918430 -18.9281140 -1 0.0000000 -1 0.0000000 0 0058 1 1 -30.3918430 -18.9281140 -1 0.0000000 -1 0.0000000 0 -29.9246720 -18.5547780 -1 0.0000000 -1 0.0000000 0 -29.4460510 -18.1960790 -1 0.0000000 -1 0.0000000 0 0059 1 1 -29.4460510 -18.1960790 -1 0.0000000 -1 0.0000000 0 -28.9564640 -17.8523280 -1 0.0000000 -1 0.0000000 0 -28.4564090 -17.5238130 -1 0.0000000 -1 0.0000000 0 0060 1 1 -28.4564090 -17.5238130 -1 0.0000000 -1 0.0000000 0 -27.9463980 -17.2108080 -1 0.0000000 -1 0.0000000 0 -27.4269430 -16.9135610 -1 0.0000000 -1 0.0000000 0 0061 1 1 -27.4269430 -16.9135610 -1 0.0000000 -1 0.0000000 0 -26.8985910 -16.6322690 -1 0.0000000 -1 0.0000000 0 -26.3618170 -16.3672470 -1 0.0000000 -1 0.0000000 0 0062 1 1 -26.3618170 -16.3672470 -1 0.0000000 -1 0.0000000 0 -25.8168760 -16.1193410 -1 0.0000000 -1 0.0000000 0 -25.2644210 -15.8886490 -1 0.0000000 -1 0.0000000 0 0063 1 1 -25.2644210 -15.8886490 -1 0.0000000 -1 0.0000000 0 -24.7067210 -15.6738580 -1 0.0000000 -1 0.0000000 0 -24.1937660 -15.4889750 -1 0.0000000 -1 0.0000000 0 0064 1 1 -24.1937660 -15.4889750 -1 0.0000000 -1 0.0000000 0 -23.6814600 -15.3152570 -1 0.0000000 -1 0.0000000 0 -23.1680960 -15.1513480 -1 0.0000000 -1 0.0000000 0 0065 1 1 -23.1680960 -15.1513480 -1 0.0000000 -1 0.0000000 0 -22.6541940 -14.9961780 -1 0.0000000 -1 0.0000000 0 -22.1392270 -14.8486600 -1 0.0000000 -1 0.0000000 0 0066 1 1 -22.1392270 -14.8486600 -1 0.0000000 -1 0.0000000 0 -21.6237560 -14.7084000 -1 0.0000000 -1 0.0000000 0 -21.1072320 -14.5748160 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 56

0067 1 1 -21.1072320 -14.5748160 -1 0.0000000 -1 0.0000000 0 -20.5900300 -14.4476180 -1 0.0000000 -1 0.0000000 0 -20.0719290 -14.3264120 -1 0.0000000 -1 0.0000000 0 0068 1 1 -20.0719290 -14.3264120 -1 0.0000000 -1 0.0000000 0 -19.5530890 -14.2109080 -1 0.0000000 -1 0.0000000 0 -19.0334590 -14.1008050 -1 0.0000000 -1 0.0000000 0 0069 1 1 -19.0334590 -14.1008050 -1 0.0000000 -1 0.0000000 0 -18.5130540 -13.9958890 -1 0.0000000 -1 0.0000000 0 -17.9918290 -13.8959670 -1 0.0000000 -1 0.0000000 0 0070 1 1 -17.9918290 -13.8959670 -1 0.0000000 -1 0.0000000 0 -17.4698810 -13.8008030 -1 0.0000000 -1 0.0000000 0 -16.9472920 -13.7101910 -1 0.0000000 -1 0.0000000 0 0071 1 1 -16.9472920 -13.7101910 -1 0.0000000 -1 0.0000000 0 -16.4240060 -13.6239530 -1 0.0000000 -1 0.0000000 0 -15.9001150 -13.5419440 -1 0.0000000 -1 0.0000000 0 0072 1 1 -15.9001150 -13.5419440 -1 0.0000000 -1 0.0000000 0 -15.3755720 -13.4640060 -1 0.0000000 -1 0.0000000 0 -14.8504690 -13.3900040 -1 0.0000000 -1 0.0000000 0 0073 1 1 -14.8504690 -13.3900040 -1 0.0000000 -1 0.0000000 0 -14.3248320 -13.3197950 -1 0.0000000 -1 0.0000000 0 -13.7986800 -13.2532360 -1 0.0000000 -1 0.0000000 0 0074 1 1 -13.7986800 -13.2532360 -1 0.0000000 -1 0.0000000 0 -13.2720240 -13.1902110 -1 0.0000000 -1 0.0000000 0 -12.7449000 -13.1306100 -1 0.0000000 -1 0.0000000 0 0075 1 1 -12.7449000 -13.1306100 -1 0.0000000 -1 0.0000000 0 -12.2173350 -13.0743260 -1 0.0000000 -1 0.0000000 0 -11.6893620 -13.0212660 -1 0.0000000 -1 0.0000000 0 0076 1 1 -11.6893620 -13.0212660 -1 0.0000000 -1 0.0000000 0 -11.1609440 -12.9712940 -1 0.0000000 -1 0.0000000 0 -10.6321650 -12.9243020 -1 0.0000000 -1 0.0000000 0 0077 1 1 -10.6321650 -12.9243020 -1 0.0000000 -1 0.0000000 0 -10.1029990 -12.8802070 -1 0.0000000 -1 0.0000000 0 -9.5734790 -12.8389350 -1 0.0000000 -1 0.0000000 0 0078 1 1 -9.5734790 -12.8389350 -1 0.0000000 -1 0.0000000 0 -9.0435910 -12.8003850 -1 0.0000000 -1 0.0000000 0 -8.5133160 -12.7644570 -1 0.0000000 -1 0.0000000 0 0079 1 1 -8.5133160 -12.7644570 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 57

-7.9827010 -12.7310960 -1 0.0000000 -1 0.0000000 0 -7.4515850 -12.7002270 -1 0.0000000 -1 0.0000000 0 0080 1 1 -7.4515850 -12.7002270 -1 0.0000000 -1 0.0000000 0 -6.9200650 -12.6717650 -1 0.0000000 -1 0.0000000 0 -6.3876870 -12.6455960 -1 0.0000000 -1 0.0000000 0 0081 1 1 -6.3876870 -12.6455960 -1 0.0000000 -1 0.0000000 0 -5.8545820 -12.6217180 -1 0.0000000 -1 0.0000000 0 -5.3146670 -12.5998890 -1 0.0000000 -1 0.0000000 0 0082 1 1 -5.3146670 -12.5998890 -1 0.0000000 -1 0.0000000 0 -4.7759650 -12.5803830 -1 0.0000000 -1 0.0000000 0 -4.2397240 -12.5631460 -1 0.0000000 -1 0.0000000 0 0083 1 1 -4.2397240 -12.5631460 -1 0.0000000 -1 0.0000000 0 -3.7053990 -12.5481030 -1 0.0000000 -1 0.0000000 0 -3.1729650 -12.5352090 -1 0.0000000 -1 0.0000000 0 0084 1 1 -3.1729650 -12.5352090 -1 0.0000000 -1 0.0000000 0 -2.6419170 -12.5243890 -1 0.0000000 -1 0.0000000 0 -2.1121110 -12.5155840 -1 0.0000000 -1 0.0000000 0 0085 1 1 -2.1121110 -12.5155840 -1 0.0000000 -1 0.0000000 0 -1.5831520 -12.5087610 -1 0.0000000 -1 0.0000000 0 -1.0548970 -12.5038980 -1 0.0000000 -1 0.0000000 0 0086 1 1 -1.0548970 -12.5038980 -1 0.0000000 -1 0.0000000 0 -0.5269560 -12.5009750 -1 0.0000000 -1 0.0000000 0 0.0000000 -12.5000000 -1 0.0000000 -1 0.0000000 0 0087 1 1 0.0000000 -12.5000000 -1 0.0000000 -1 0.0000000 0 0.5269560 -12.5009750 -1 0.0000000 -1 0.0000000 0 1.0548970 -12.5038980 -1 0.0000000 -1 0.0000000 0 0088 1 1 1.0548970 -12.5038980 -1 0.0000000 -1 0.0000000 0 1.5831520 -12.5087610 -1 0.0000000 -1 0.0000000 0 2.1121110 -12.5155840 -1 0.0000000 -1 0.0000000 0 0089 1 1 2.1121110 -12.5155840 -1 0.0000000 -1 0.0000000 0 2.6419170 -12.5243890 -1 0.0000000 -1 0.0000000 0 3.1729650 -12.5352090 -1 0.0000000 -1 0.0000000 0 0090 1 1 3.1729650 -12.5352090 -1 0.0000000 -1 0.0000000 0 3.7053990 -12.5481030 -1 0.0000000 -1 0.0000000 0 4.2397240 -12.5631460 -1 0.0000000 -1 0.0000000 0 0091 1 1 4.2397240 -12.5631460 -1 0.0000000 -1 0.0000000 0 4.7759650 -12.5803830 -1 0.0000000 -1 0.0000000 0 5.3146670 -12.5998890 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 58

0092 1 1 5.3146670 -12.5998890 -1 0.0000000 -1 0.0000000 0 5.8545820 -12.6217180 -1 0.0000000 -1 0.0000000 0 6.3876870 -12.6455960 -1 0.0000000 -1 0.0000000 0 0093 1 1 6.3876870 -12.6455960 -1 0.0000000 -1 0.0000000 0 6.9200650 -12.6717650 -1 0.0000000 -1 0.0000000 0 7.4515850 -12.7002270 -1 0.0000000 -1 0.0000000 0 0094 1 1 7.4515850 -12.7002270 -1 0.0000000 -1 0.0000000 0 7.9827010 -12.7310960 -1 0.0000000 -1 0.0000000 0 8.5133160 -12.7644570 -1 0.0000000 -1 0.0000000 0 0095 1 1 8.5133160 -12.7644570 -1 0.0000000 -1 0.0000000 0 9.0435910 -12.8003850 -1 0.0000000 -1 0.0000000 0 9.5734790 -12.8389350 -1 0.0000000 -1 0.0000000 0 0096 1 1 9.5734790 -12.8389350 -1 0.0000000 -1 0.0000000 0 10.1029990 -12.8802070 -1 0.0000000 -1 0.0000000 0 10.6321650 -12.9243020 -1 0.0000000 -1 0.0000000 0 0097 1 1 10.6321650 -12.9243020 -1 0.0000000 -1 0.0000000 0 11.1609440 -12.9712940 -1 0.0000000 -1 0.0000000 0 11.6893620 -13.0212660 -1 0.0000000 -1 0.0000000 0 0098 1 1 11.6893620 -13.0212660 -1 0.0000000 -1 0.0000000 0 12.2173350 -13.0743260 -1 0.0000000 -1 0.0000000 0 12.7449000 -13.1306100 -1 0.0000000 -1 0.0000000 0 0099 1 1 12.7449000 -13.1306100 -1 0.0000000 -1 0.0000000 0 13.2720240 -13.1902110 -1 0.0000000 -1 0.0000000 0 13.7986800 -13.2532360 -1 0.0000000 -1 0.0000000 0 0100 1 1 13.7986800 -13.2532360 -1 0.0000000 -1 0.0000000 0 14.3248320 -13.3197950 -1 0.0000000 -1 0.0000000 0 14.8504690 -13.3900040 -1 0.0000000 -1 0.0000000 0 0101 1 1 14.8504690 -13.3900040 -1 0.0000000 -1 0.0000000 0 15.3755720 -13.4640060 -1 0.0000000 -1 0.0000000 0 15.9001150 -13.5419440 -1 0.0000000 -1 0.0000000 0 0102 1 1 15.9001150 -13.5419440 -1 0.0000000 -1 0.0000000 0 16.4240060 -13.6239530 -1 0.0000000 -1 0.0000000 0 16.9472920 -13.7101910 -1 0.0000000 -1 0.0000000 0 0103 1 1 16.9472920 -13.7101910 -1 0.0000000 -1 0.0000000 0 17.4698810 -13.8008030 -1 0.0000000 -1 0.0000000 0 17.9918290 -13.8959670 -1 0.0000000 -1 0.0000000 0 0104 1 1


UNCLASSIFIED 59

17.9918290 -13.8959670 -1 0.0000000 -1 0.0000000 0 18.5130540 -13.9958890 -1 0.0000000 -1 0.0000000 0 19.0334590 -14.1008050 -1 0.0000000 -1 0.0000000 0 0105 1 1 19.0334590 -14.1008050 -1 0.0000000 -1 0.0000000 0 19.5530890 -14.2109080 -1 0.0000000 -1 0.0000000 0 20.0719290 -14.3264120 -1 0.0000000 -1 0.0000000 0 0106 1 1 20.0719290 -14.3264120 -1 0.0000000 -1 0.0000000 0 20.5900300 -14.4476180 -1 0.0000000 -1 0.0000000 0 21.1072320 -14.5748160 -1 0.0000000 -1 0.0000000 0 0107 1 1 21.1072320 -14.5748160 -1 0.0000000 -1 0.0000000 0 21.6237560 -14.7084000 -1 0.0000000 -1 0.0000000 0 22.1392270 -14.8486600 -1 0.0000000 -1 0.0000000 0 0108 1 1 22.1392270 -14.8486600 -1 0.0000000 -1 0.0000000 0 22.6541940 -14.9961780 -1 0.0000000 -1 0.0000000 0 23.1680960 -15.1513480 -1 0.0000000 -1 0.0000000 0 0109 1 1 23.1680960 -15.1513480 -1 0.0000000 -1 0.0000000 0 23.6814600 -15.3152570 -1 0.0000000 -1 0.0000000 0 24.1937660 -15.4889750 -1 0.0000000 -1 0.0000000 0 0110 1 1 24.1937660 -15.4889750 -1 0.0000000 -1 0.0000000 0 24.7067210 -15.6738580 -1 0.0000000 -1 0.0000000 0 25.2644210 -15.8886490 -1 0.0000000 -1 0.0000000 0 0111 1 1 25.2644210 -15.8886490 -1 0.0000000 -1 0.0000000 0 25.8168760 -16.1193410 -1 0.0000000 -1 0.0000000 0 26.3618170 -16.3672470 -1 0.0000000 -1 0.0000000 0 0112 1 1 26.3618170 -16.3672470 -1 0.0000000 -1 0.0000000 0 26.8985910 -16.6322690 -1 0.0000000 -1 0.0000000 0 27.4269430 -16.9135610 -1 0.0000000 -1 0.0000000 0 0113 1 1 27.4269430 -16.9135610 -1 0.0000000 -1 0.0000000 0 27.9463980 -17.2108080 -1 0.0000000 -1 0.0000000 0 28.4564090 -17.5238130 -1 0.0000000 -1 0.0000000 0 0114 1 1 28.4564090 -17.5238130 -1 0.0000000 -1 0.0000000 0 28.9564640 -17.8523280 -1 0.0000000 -1 0.0000000 0 29.4460510 -18.1960790 -1 0.0000000 -1 0.0000000 0 0115 1 1 29.4460510 -18.1960790 -1 0.0000000 -1 0.0000000 0 29.9246720 -18.5547780 -1 0.0000000 -1 0.0000000 0 30.3918430 -18.9281140 -1 0.0000000 -1 0.0000000 0 0116 1 1 30.3918430 -18.9281140 -1 0.0000000 -1 0.0000000 0 30.8470810 -19.3157570 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 60

31.2899290 -19.7173620 -1 0.0000000 -1 0.0000000 0 0117 1 1 31.2899290 -19.7173620 -1 0.0000000 -1 0.0000000 0 31.7199390 -20.1325620 -1 0.0000000 -1 0.0000000 0 32.1366780 -20.5609680 -1 0.0000000 -1 0.0000000 0 0118 1 1 32.1366780 -20.5609680 -1 0.0000000 -1 0.0000000 0 32.5397330 -21.0021790 -1 0.0000000 -1 0.0000000 0 32.9287130 -21.4557740 -1 0.0000000 -1 0.0000000 0 0119 1 1 32.9287130 -21.4557740 -1 0.0000000 -1 0.0000000 0 33.3032360 -21.9213120 -1 0.0000000 -1 0.0000000 0 33.6629540 -22.3983410 -1 0.0000000 -1 0.0000000 0 0120 1 1 33.6629540 -22.3983410 -1 0.0000000 -1 0.0000000 0 34.0075320 -22.8863920 -1 0.0000000 -1 0.0000000 0 34.3366610 -23.3849790 -1 0.0000000 -1 0.0000000 0 0121 1 1 34.3366610 -23.3849790 -1 0.0000000 -1 0.0000000 0 34.6500560 -23.8936100 -1 0.0000000 -1 0.0000000 0 34.9474520 -24.4117710 -1 0.0000000 -1 0.0000000 0 0122 1 1 34.9474520 -24.4117710 -1 0.0000000 -1 0.0000000 0 35.2286050 -24.9389450 -1 0.0000000 -1 0.0000000 0 35.4933050 -25.4746060 -1 0.0000000 -1 0.0000000 0 0123 1 1 35.4933050 -25.4746060 -1 0.0000000 -1 0.0000000 0 35.7413540 -26.0182160 -1 0.0000000 -1 0.0000000 0 35.9725840 -26.5692330 -1 0.0000000 -1 0.0000000 0 0124 1 1 35.9725840 -26.5692330 -1 0.0000000 -1 0.0000000 0 36.1868470 -27.1271100 -1 0.0000000 -1 0.0000000 0 36.3840200 -27.6912950 -1 0.0000000 -1 0.0000000 0 0125 1 1 36.3840200 -27.6912950 -1 0.0000000 -1 0.0000000 0 36.5639950 -28.2612320 -1 0.0000000 -1 0.0000000 0 36.7266910 -28.8363660 -1 0.0000000 -1 0.0000000 0 0126 1 1 36.7266910 -28.8363660 -1 0.0000000 -1 0.0000000 0 36.8720530 -29.4161390 -1 0.0000000 -1 0.0000000 0 37.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 0127 1 4 37.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 49.5000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 62.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 -2 0 1 0128 1 4 62.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 -2 0 1 92.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 0 122.0000000 -30.0000000 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 61

0129 1 4 122.0000000 -30.0000000 -1 100.0000000 -1 0.0000000 0 122.0000000 -15.0000000 -1 100.0000000 -1 0.0000000 0 122.0000000 0.0000000 -1 100.0000000 -1 0.0000000 -2 0 1 0130 1 4 122.0000000 0.0000000 -1 100.0000000 -1 0.0000000 -2 0 1 122.0000000 15.0000000 -1 100.0000000 -1 0.0000000 0 122.0000000 30.0000000 -1 100.0000000 -1 0.0000000 0 0131 1 4 122.0000000 30.0000000 -1 0.0000000 -1 0.0000000 0 92.0000000 30.0000000 -1 0.0000000 -1 0.0000000 0 62.0000000 30.0000000 -1 0.0000000 -1 0.0000000 -2 0 1 0132 1 4 62.0000000 30.0000000 -1 0.0000000 -1 0.0000000 -2 0 1 49.5000000 30.0000000 -1 0.0000000 -1 0.0000000 0 37.0000000 30.0000000 -1 0.0000000 -1 0.0000000 0 0133 1 2 37.0000000 30.0000000 -1 0.0000000 -1 0.0000000 0 36.8720530 29.4161390 -1 0.0000000 -1 0.0000000 0 36.7266910 28.8363660 -1 0.0000000 -1 0.0000000 0 0134 1 2 36.7266910 28.8363660 -1 0.0000000 -1 0.0000000 0 36.5639950 28.2612320 -1 0.0000000 -1 0.0000000 0 36.3840200 27.6912950 -1 0.0000000 -1 0.0000000 0 0135 1 2 36.3840200 27.6912950 -1 0.0000000 -1 0.0000000 0 36.1868470 27.1271100 -1 0.0000000 -1 0.0000000 0 35.9725840 26.5692330 -1 0.0000000 -1 0.0000000 0 0136 1 2 35.9725840 26.5692330 -1 0.0000000 -1 0.0000000 0 35.7413540 26.0182160 -1 0.0000000 -1 0.0000000 0 35.4933050 25.4746060 -1 0.0000000 -1 0.0000000 0 0137 1 2 35.4933050 25.4746060 -1 0.0000000 -1 0.0000000 0 35.2286050 24.9389450 -1 0.0000000 -1 0.0000000 0 34.9474520 24.4117710 -1 0.0000000 -1 0.0000000 0 0138 1 2 34.9474520 24.4117710 -1 0.0000000 -1 0.0000000 0 34.6500560 23.8936100 -1 0.0000000 -1 0.0000000 0 34.3366610 23.3849790 -1 0.0000000 -1 0.0000000 0 0139 1 2 34.3366610 23.3849790 -1 0.0000000 -1 0.0000000 0 34.0075320 22.8863920 -1 0.0000000 -1 0.0000000 0 33.6629540 22.3983410 -1 0.0000000 -1 0.0000000 0 0140 1 2 33.6629540 22.3983410 -1 0.0000000 -1 0.0000000 0 33.3032360 21.9213120 -1 0.0000000 -1 0.0000000 0 32.9287130 21.4557740 -1 0.0000000 -1 0.0000000 0 0141 1 2 32.9287130 21.4557740 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 62

32.5397330 21.0021790 -1 0.0000000 -1 0.0000000 0 32.1366780 20.5609680 -1 0.0000000 -1 0.0000000 0 0142 1 2 32.1366780 20.5609680 -1 0.0000000 -1 0.0000000 0 31.7199390 20.1325620 -1 0.0000000 -1 0.0000000 0 31.2899290 19.7173620 -1 0.0000000 -1 0.0000000 0 0143 1 2 31.2899290 19.7173620 -1 0.0000000 -1 0.0000000 0 30.8470810 19.3157570 -1 0.0000000 -1 0.0000000 0 30.3918430 18.9281140 -1 0.0000000 -1 0.0000000 0 0144 1 2 30.3918430 18.9281140 -1 0.0000000 -1 0.0000000 0 29.9246720 18.5547780 -1 0.0000000 -1 0.0000000 0 29.4460510 18.1960790 -1 0.0000000 -1 0.0000000 0 0145 1 2 29.4460510 18.1960790 -1 0.0000000 -1 0.0000000 0 28.9564640 17.8523280 -1 0.0000000 -1 0.0000000 0 28.4564090 17.5238130 -1 0.0000000 -1 0.0000000 0 0146 1 2 28.4564090 17.5238130 -1 0.0000000 -1 0.0000000 0 27.9463980 17.2108080 -1 0.0000000 -1 0.0000000 0 27.4269430 16.9135610 -1 0.0000000 -1 0.0000000 0 0147 1 2 27.4269430 16.9135610 -1 0.0000000 -1 0.0000000 0 26.8985910 16.6322690 -1 0.0000000 -1 0.0000000 0 26.3618170 16.3672470 -1 0.0000000 -1 0.0000000 0 0148 1 2 26.3618170 16.3672470 -1 0.0000000 -1 0.0000000 0 25.8168760 16.1193410 -1 0.0000000 -1 0.0000000 0 25.2644210 15.8886490 -1 0.0000000 -1 0.0000000 0 0149 1 2 25.2644210 15.8886490 -1 0.0000000 -1 0.0000000 0 24.7067210 15.6738580 -1 0.0000000 -1 0.0000000 0 24.1937660 15.4889750 -1 0.0000000 -1 0.0000000 0 0150 1 2 24.1937660 15.4889750 -1 0.0000000 -1 0.0000000 0 23.6814600 15.3152570 -1 0.0000000 -1 0.0000000 0 23.1680960 15.1513480 -1 0.0000000 -1 0.0000000 0 0151 1 2 23.1680960 15.1513480 -1 0.0000000 -1 0.0000000 0 22.6541940 14.9961780 -1 0.0000000 -1 0.0000000 0 22.1392270 14.8486600 -1 0.0000000 -1 0.0000000 0 0152 1 2 22.1392270 14.8486600 -1 0.0000000 -1 0.0000000 0 21.6237560 14.7084000 -1 0.0000000 -1 0.0000000 0 21.1072320 14.5748160 -1 0.0000000 -1 0.0000000 0 0153 1 2 21.1072320 14.5748160 -1 0.0000000 -1 0.0000000 0 20.5900300 14.4476180 -1 0.0000000 -1 0.0000000 0 20.0719290 14.3264120 -1 0.0000000 -1 0.0000000 0


UNCLASSIFIED 63

0154 1 2 20.0719290 14.3264120 -1 0.0000000 -1 0.0000000 0 19.5530890 14.2109080 -1 0.0000000 -1 0.0000000 0 19.0334590 14.1008050 -1 0.0000000 -1 0.0000000 0 0155 1 2 19.0334590 14.1008050 -1 0.0000000 -1 0.0000000 0 18.5130540 13.9958890 -1 0.0000000 -1 0.0000000 0 17.9918290 13.8959670 -1 0.0000000 -1 0.0000000 0 0156 1 2 17.9918290 13.8959670 -1 0.0000000 -1 0.0000000 0 17.4698810 13.8008030 -1 0.0000000 -1 0.0000000 0 16.9472920 13.7101910 -1 0.0000000 -1 0.0000000 0 0157 1 2 16.9472920 13.7101910 -1 0.0000000 -1 0.0000000 0 16.4240060 13.6239530 -1 0.0000000 -1 0.0000000 0 15.9001150 13.5419440 -1 0.0000000 -1 0.0000000 0 0158 1 2 15.9001150 13.5419440 -1 0.0000000 -1 0.0000000 0 15.3755720 13.4640060 -1 0.0000000 -1 0.0000000 0 14.8504690 13.3900040 -1 0.0000000 -1 0.0000000 0 0159 1 2 14.8504690 13.3900040 -1 0.0000000 -1 0.0000000 0 14.3248320 13.3197950 -1 0.0000000 -1 0.0000000 0 13.7986800 13.2532360 -1 0.0000000 -1 0.0000000 0 0160 1 2 13.7986800 13.2532360 -1 0.0000000 -1 0.0000000 0 13.2720240 13.1902110 -1 0.0000000 -1 0.0000000 0 12.7449000 13.1306100 -1 0.0000000 -1 0.0000000 0 0161 1 2 12.7449000 13.1306100 -1 0.0000000 -1 0.0000000 0 12.2173350 13.0743260 -1 0.0000000 -1 0.0000000 0 11.6893620 13.0212660 -1 0.0000000 -1 0.0000000 0 0162 1 2 11.6893620 13.0212660 -1 0.0000000 -1 0.0000000 0 11.1609440 12.9712940 -1 0.0000000 -1 0.0000000 0 10.6321650 12.9243020 -1 0.0000000 -1 0.0000000 0 0163 1 2 10.6321650 12.9243020 -1 0.0000000 -1 0.0000000 0 10.1029990 12.8802070 -1 0.0000000 -1 0.0000000 0 9.5734790 12.8389350 -1 0.0000000 -1 0.0000000 0 0164 1 2 9.5734790 12.8389350 -1 0.0000000 -1 0.0000000 0 9.0435910 12.8003850 -1 0.0000000 -1 0.0000000 0 8.5133160 12.7644570 -1 0.0000000 -1 0.0000000 0 0165 1 2 8.5133160 12.7644570 -1 0.0000000 -1 0.0000000 0 7.9827010 12.7310960 -1 0.0000000 -1 0.0000000 0 7.4515850 12.7002270 -1 0.0000000 -1 0.0000000 0 0166 1 2


UNCLASSIFIED 64

7.4515850 12.7002270 -1 0.0000000 -1 0.0000000 0 6.9200650 12.6717650 -1 0.0000000 -1 0.0000000 0 6.3876870 12.6455960 -1 0.0000000 -1 0.0000000 0 0167 1 2 6.3876870 12.6455960 -1 0.0000000 -1 0.0000000 0 5.8545820 12.6217180 -1 0.0000000 -1 0.0000000 0 5.3146670 12.5998890 -1 0.0000000 -1 0.0000000 0 0168 1 2 5.3146670 12.5998890 -1 0.0000000 -1 0.0000000 0 4.7759650 12.5803830 -1 0.0000000 -1 0.0000000 0 4.2397240 12.5631460 -1 0.0000000 -1 0.0000000 0 0169 1 2 4.2397240 12.5631460 -1 0.0000000 -1 0.0000000 0 3.7053990 12.5481030 -1 0.0000000 -1 0.0000000 0 3.1729650 12.5352090 -1 0.0000000 -1 0.0000000 0 0170 1 2 3.1729650 12.5352090 -1 0.0000000 -1 0.0000000 0 2.6419170 12.5243890 -1 0.0000000 -1 0.0000000 0 2.1121110 12.5155840 -1 0.0000000 -1 0.0000000 0 0171 1 2 2.1121110 12.5155840 -1 0.0000000 -1 0.0000000 0 1.5831520 12.5087610 -1 0.0000000 -1 0.0000000 0 1.0548970 12.5038980 -1 0.0000000 -1 0.0000000 0 0172 1 16 1.0548970 12.5038980 -1 0.0000000 -1 0.0000000 0 0.5269560 12.5009750 -1 0.0000000 -1 0.0000000 0 0.0000000 12.5000000 -1 0.0000000 -1 0.0000000 1 --------------------------------------------------------------------------------------


UNCLASSIFIED 65

Appendix G:

IGES file of coordinates for Modified Constant-Stress Coupon

The following input file can also be found stored in Objective folder fAV1044714. The name of the file is Al_mod_optimal_3D_msmth_smoothed_002.igs.

MSC.Patran generated IGES File from database S0000001 /home/username/abaqus/abopt/fillet3dmod/Al_mod_optimal_3D_msmth_iges_002S0000002 .d S0000003 ,,22HMSC.Patran IGES Access,80H/home/username/abaqus/abopt/fillet3dmod/AG0000001 l_mod_optimal_3D_msmth_smoothed_002.igs,35HMSC.Patran 19.0.132332 MSC.SoG0000002 ftware,11H19.0.132332, G0000003 32,38,6,,,22HMSC.Patran IGES Export, G0000004 1.0, 2,2HMM,1,0,13H140501.142551,0.200000E-04,37., G0000005 8Husername,23HMSC.Patran User's Group, G0000006 11,0,13H140501.142551,; G0000007 116 1 2 2 0 0 0 000000000D0000001 116 0 0 1 0 0 0POINT 1D0000002 116 2 2 2 0 0 0 000000000D0000003 116 0 0 1 0 0 0POINT 2D0000004 116 3 2 2 0 0 0 000000000D0000005 116 0 0 1 0 0 0POINT 3D0000006 116 4 2 2 0 0 0 000000000D0000007 116 0 0 1 0 0 0POINT 4D0000008 116 5 2 2 0 0 0 000000000D0000009 116 0 0 1 0 0 0POINT 5D0000010 116 6 2 2 0 0 0 000000000D0000011 116 0 0 1 0 0 0POINT 6D0000012 116 7 2 2 0 0 0 000000000D0000013 116 0 0 1 0 0 0POINT 7D0000014 116 8 2 2 0 0 0 000000000D0000015 116 0 0 1 0 0 0POINT 8D0000016 116 9 2 2 0 0 0 000000000D0000017 116 0 0 1 0 0 0POINT 9D0000018 116 10 2 2 0 0 0 000000000D0000019 116 0 0 1 0 0 0POINT 10D0000020 116 11 2 2 0 0 0 000000000D0000021 116 0 0 1 0 0 0POINT 11D0000022 116 12 2 2 0 0 0 000000000D0000023 116 0 0 1 0 0 0POINT 12D0000024 116 13 2 2 0 0 0 000000000D0000025 116 0 0 1 0 0 0POINT 13D0000026 116 14 2 2 0 0 0 000000000D0000027 116 0 0 1 0 0 0POINT 14D0000028 116 15 2 2 0 0 0 000000000D0000029 116 0 0 1 0 0 0POINT 15D0000030 116 16 2 2 0 0 0 000000000D0000031 116 0 0 1 0 0 0POINT 16D0000032 116 17 2 2 0 0 0 000000000D0000033 116 0 0 1 0 0 0POINT 17D0000034 116 18 2 2 0 0 0 000000000D0000035 116 0 0 1 0 0 0POINT 18D0000036 116 19 2 2 0 0 0 000000000D0000037


UNCLASSIFIED 66

116 0 0 1 0 0 0POINT 19D0000038 116 20 2 2 0 0 0 000000000D0000039 116 0 0 1 0 0 0POINT 20D0000040 116 21 2 2 0 0 0 000000000D0000041 116 0 0 1 0 0 0POINT 21D0000042 116 22 2 2 0 0 0 000000000D0000043 116 0 0 1 0 0 0POINT 22D0000044 116 23 2 2 0 0 0 000000000D0000045 116 0 0 1 0 0 0POINT 23D0000046 116 24 2 2 0 0 0 000000000D0000047 116 0 0 1 0 0 0POINT 24D0000048 116 25 2 2 0 0 0 000000000D0000049 116 0 0 1 0 0 0POINT 25D0000050 116 26 2 2 0 0 0 000000000D0000051 116 0 0 1 0 0 0POINT 26D0000052 116 27 2 2 0 0 0 000000000D0000053 116 0 0 1 0 0 0POINT 27D0000054 116 28 2 2 0 0 0 000000000D0000055 116 0 0 1 0 0 0POINT 28D0000056 116 29 2 2 0 0 0 000000000D0000057 116 0 0 1 0 0 0POINT 29D0000058 116 30 2 2 0 0 0 000000000D0000059 116 0 0 1 0 0 0POINT 30D0000060 116 31 2 2 0 0 0 000000000D0000061 116 0 0 1 0 0 0POINT 31D0000062 116 32 2 2 0 0 0 000000000D0000063 116 0 0 1 0 0 0POINT 32D0000064 116 33 2 2 0 0 0 000000000D0000065 116 0 0 1 0 0 0POINT 33D0000066 116 34 2 2 0 0 0 000000000D0000067 116 0 0 1 0 0 0POINT 34D0000068 116 35 2 2 0 0 0 000000000D0000069 116 0 0 1 0 0 0POINT 35D0000070 116 36 2 2 0 0 0 000000000D0000071 116 0 0 1 0 0 0POINT 36D0000072 116 37 2 2 0 0 0 000000000D0000073 116 0 0 1 0 0 0POINT 37D0000074 116 38 2 2 0 0 0 000000000D0000075 116 0 0 1 0 0 0POINT 38D0000076 116 39 2 2 0 0 0 000000000D0000077 116 0 0 1 0 0 0POINT 39D0000078 116 40 2 2 0 0 0 000000000D0000079 116 0 0 1 0 0 0POINT 40D0000080 116 41 2 2 0 0 0 000000000D0000081 116 0 0 1 0 0 0POINT 41D0000082 116 42 2 2 0 0 0 000000000D0000083 116 0 0 1 0 0 0POINT 42D0000084 116 43 2 2 0 0 0 000000000D0000085 116 0 0 1 0 0 0POINT 43D0000086 116 44 2 2 0 0 0 000000000D0000087 116 0 0 1 0 0 0POINT 44D0000088 116 45 2 2 0 0 0 000000000D0000089 116 0 0 1 0 0 0POINT 45D0000090 116 46 2 2 0 0 0 000000000D0000091 116 0 0 1 0 0 0POINT 46D0000092 116 47 2 2 0 0 0 000000000D0000093 116 0 0 1 0 0 0POINT 47D0000094 116 48 2 2 0 0 0 000000000D0000095 116 0 0 1 0 0 0POINT 48D0000096 116 49 2 2 0 0 0 000000000D0000097


UNCLASSIFIED 67



UNCLASSIFIED 68



UNCLASSIFIED 69



UNCLASSIFIED 70

116 0 0 1 0 0 0POINT 139D0000278 116 140 2 2 0 0 0 000000000D0000279 116 0 0 1 0 0 0POINT 140D0000280 116 141 2 2 0 0 0 000000000D0000281 116 0 0 1 0 0 0POINT 141D0000282 116 142 2 2 0 0 0 000000000D0000283 116 0 0 1 0 0 0POINT 142D0000284 116 143 2 2 0 0 0 000000000D0000285 116 0 0 1 0 0 0POINT 143D0000286 116 144 2 2 0 0 0 000000000D0000287 116 0 0 1 0 0 0POINT 144D0000288 116 145 2 2 0 0 0 000000000D0000289 116 0 0 1 0 0 0POINT 145D0000290 116 146 2 2 0 0 0 000000000D0000291 116 0 0 1 0 0 0POINT 146D0000292 116 147 2 2 0 0 0 000000000D0000293 116 0 0 1 0 0 0POINT 147D0000294 116 148 2 2 0 0 0 000000000D0000295 116 0 0 1 0 0 0POINT 148D0000296 116 149 2 2 0 0 0 000000000D0000297 116 0 0 1 0 0 0POINT 149D0000298 116 150 2 2 0 0 0 000000000D0000299 116 0 0 1 0 0 0POINT 150D0000300 116 151 2 2 0 0 0 000000000D0000301 116 0 0 1 0 0 0POINT 151D0000302 116 152 2 2 0 0 0 000000000D0000303 116 0 0 1 0 0 0POINT 152D0000304 116 153 2 2 0 0 0 000000000D0000305 116 0 0 1 0 0 0POINT 153D0000306 116 154 2 2 0 0 0 000000000D0000307 116 0 0 1 0 0 0POINT 154D0000308 116 155 2 2 0 0 0 000000000D0000309 116 0 0 1 0 0 0POINT 155D0000310 116 156 2 2 0 0 0 000000000D0000311 116 0 0 1 0 0 0POINT 156D0000312 116 157 2 2 0 0 0 000000000D0000313 116 0 0 1 0 0 0POINT 157D0000314 116 158 2 2 0 0 0 000000000D0000315 116 0 0 1 0 0 0POINT 158D0000316 116 159 2 2 0 0 0 000000000D0000317 116 0 0 1 0 0 0POINT 159D0000318 116 160 2 2 0 0 0 000000000D0000319 116 0 0 1 0 0 0POINT 160D0000320 116 161 2 2 0 0 0 000000000D0000321 116 0 0 1 0 0 0POINT 161D0000322 124 162 2 1 0 0 0 000010000D0000323 124 0 0 4 0 0 0MATRIX 1D0000324 100 166 2 1 0 0 323 000000000D0000325 100 0 0 3 0 0 0CIRC ARC 1D0000326 124 169 2 1 0 0 0 000010000D0000327 124 0 0 4 0 0 0MATRIX 2D0000328 100 173 2 1 0 0 327 000000000D0000329 100 0 0 3 0 0 0CIRC ARC 2D0000330 124 176 2 1 0 0 0 000010000D0000331 124 0 0 4 0 0 0MATRIX 3D0000332 100 180 2 1 0 0 331 000000000D0000333 100 0 0 3 0 0 0CIRC ARC 3D0000334 124 183 2 1 0 0 0 000010000D0000335 124 0 0 4 0 0 0MATRIX 4D0000336 100 187 2 1 0 0 335 000000000D0000337


UNCLASSIFIED 71

100 0 0 3 0 0 0CIRC ARC 4D0000338 124 190 2 1 0 0 0 000010000D0000339 124 0 0 4 0 0 0MATRIX 5D0000340 100 194 2 1 0 0 339 000000000D0000341 100 0 0 3 0 0 0CIRC ARC 5D0000342 124 197 2 1 0 0 0 000010000D0000343 124 0 0 4 0 0 0MATRIX 6D0000344 100 201 2 1 0 0 343 000000000D0000345 100 0 0 3 0 0 0CIRC ARC 6D0000346 124 204 2 1 0 0 0 000010000D0000347 124 0 0 4 0 0 0MATRIX 7D0000348 100 208 2 1 0 0 347 000000000D0000349 100 0 0 3 0 0 0CIRC ARC 7D0000350 124 211 2 1 0 0 0 000010000D0000351 124 0 0 4 0 0 0MATRIX 8D0000352 100 215 2 1 0 0 351 000000000D0000353 100 0 0 3 0 0 0CIRC ARC 8D0000354 124 218 2 1 0 0 0 000010000D0000355 124 0 0 4 0 0 0MATRIX 9D0000356 100 222 2 1 0 0 355 000000000D0000357 100 0 0 3 0 0 0CIRC ARC 9D0000358 124 225 2 1 0 0 0 000010000D0000359 124 0 0 4 0 0 0MATRIX 10D0000360 100 229 2 1 0 0 359 000000000D0000361 100 0 0 3 0 0 0CIRC ARC 10D0000362 124 232 2 1 0 0 0 000010000D0000363 124 0 0 4 0 0 0MATRIX 11D0000364 100 236 2 1 0 0 363 000000000D0000365 100 0 0 3 0 0 0CIRC ARC 11D0000366 124 239 2 1 0 0 0 000010000D0000367 124 0 0 4 0 0 0MATRIX 12D0000368 100 243 2 1 0 0 367 000000000D0000369 100 0 0 3 0 0 0CIRC ARC 12D0000370 124 246 2 1 0 0 0 000010000D0000371 124 0 0 4 0 0 0MATRIX 13D0000372 100 250 2 1 0 0 371 000000000D0000373 100 0 0 3 0 0 0CIRC ARC 13D0000374 124 253 2 1 0 0 0 000010000D0000375 124 0 0 4 0 0 0MATRIX 14D0000376 100 257 2 1 0 0 375 000000000D0000377 100 0 0 3 0 0 0CIRC ARC 14D0000378 124 260 2 1 0 0 0 000010000D0000379 124 0 0 4 0 0 0MATRIX 15D0000380 100 264 2 1 0 0 379 000000000D0000381 100 0 0 3 0 0 0CIRC ARC 15D0000382 124 267 2 1 0 0 0 000010000D0000383 124 0 0 4 0 0 0MATRIX 16D0000384 100 271 2 1 0 0 383 000000000D0000385 100 0 0 3 0 0 0CIRC ARC 16D0000386 124 274 2 1 0 0 0 000010000D0000387 124 0 0 4 0 0 0MATRIX 17D0000388 100 278 2 1 0 0 387 000000000D0000389 100 0 0 3 0 0 0CIRC ARC 17D0000390 124 281 2 1 0 0 0 000010000D0000391 124 0 0 4 0 0 0MATRIX 18D0000392 100 285 2 1 0 0 391 000000000D0000393 100 0 0 3 0 0 0CIRC ARC 18D0000394 124 288 2 1 0 0 0 000010000D0000395 124 0 0 4 0 0 0MATRIX 19D0000396 100 292 2 1 0 0 395 000000000D0000397


UNCLASSIFIED 72



UNCLASSIFIED 73



UNCLASSIFIED 74



UNCLASSIFIED 75



UNCLASSIFIED 76



UNCLASSIFIED 77



UNCLASSIFIED 78



UNCLASSIFIED 79



UNCLASSIFIED 80



UNCLASSIFIED 81

100 0 0 3 0 0 0CIRC ARC 154D0000938 124 1240 2 1 0 0 0 000010000D0000939 124 0 0 4 0 0 0MATRIX 155D0000940 100 1244 2 1 0 0 939 000000000D0000941 100 0 0 3 0 0 0CIRC ARC 155D0000942 124 1247 2 1 0 0 0 000010000D0000943 124 0 0 4 0 0 0MATRIX 156D0000944 100 1251 2 1 0 0 943 000000000D0000945 100 0 0 3 0 0 0CIRC ARC 156D0000946 124 1254 2 1 0 0 0 000010000D0000947 124 0 0 4 0 0 0MATRIX 157D0000948 100 1258 2 1 0 0 947 000000000D0000949 100 0 0 3 0 0 0CIRC ARC 157D0000950 124 1261 2 1 0 0 0 000010000D0000951 124 0 0 4 0 0 0MATRIX 158D0000952 100 1265 2 1 0 0 951 000000000D0000953 100 0 0 3 0 0 0CIRC ARC 158D0000954 124 1268 2 1 0 0 0 000010000D0000955 124 0 0 4 0 0 0MATRIX 159D0000956 100 1272 2 1 0 0 955 000000000D0000957 100 0 0 3 0 0 0CIRC ARC 159D0000958 124 1275 2 1 0 0 0 000010000D0000959 124 0 0 4 0 0 0MATRIX 160D0000960 100 1279 2 1 0 0 959 000000000D0000961 100 0 0 3 0 0 0CIRC ARC 160D0000962 116,-0.370000000E+02, 0.300000000E+02, 0.000000000E+00; 1P0000001 116,-0.368720512E+02, 0.294161396E+02, 0.000000000E+00; 3P0000002 116,-0.367266922E+02, 0.288363667E+02, 0.000000000E+00; 5P0000003 116,-0.365639954E+02, 0.282612324E+02, 0.000000000E+00; 7P0000004 116,-0.363840218E+02, 0.276912956E+02, 0.000000000E+00; 9P0000005 116,-0.361868477E+02, 0.271271095E+02, 0.000000000E+00; 11P0000006 116,-0.359725838E+02, 0.265692329E+02, 0.000000000E+00; 13P0000007 116,-0.357413559E+02, 0.260182152E+02, 0.000000000E+00; 15P0000008 116,-0.354933052E+02, 0.254746056E+02, 0.000000000E+00; 17P0000009 116,-0.352286034E+02, 0.249389458E+02, 0.000000000E+00; 19P0000010 116,-0.349474525E+02, 0.244117718E+02, 0.000000000E+00; 21P0000011 116,-0.346500549E+02, 0.238936100E+02, 0.000000000E+00; 23P0000012 116,-0.343366623E+02, 0.233849792E+02, 0.000000000E+00; 25P0000013 116,-0.340075302E+02, 0.228863926E+02, 0.000000000E+00; 27P0000014 116,-0.336629524E+02, 0.223983402E+02, 0.000000000E+00; 29P0000015 116,-0.333032341E+02, 0.219213123E+02, 0.000000000E+00; 31P0000016 116,-0.329287148E+02, 0.214557743E+02, 0.000000000E+00; 33P0000017 116,-0.325397339E+02, 0.210021782E+02, 0.000000000E+00; 35P0000018 116,-0.321366768E+02, 0.205609684E+02, 0.000000000E+00; 37P0000019 116,-0.317199383E+02, 0.201325626E+02, 0.000000000E+00; 39P0000020 116,-0.312899284E+02, 0.197173615E+02, 0.000000000E+00; 41P0000021 116,-0.308470802E+02, 0.193157578E+02, 0.000000000E+00; 43P0000022 116,-0.303918438E+02, 0.189281139E+02, 0.000000000E+00; 45P0000023 116,-0.299246712E+02, 0.185547771E+02, 0.000000000E+00; 47P0000024 116,-0.294460506E+02, 0.181960793E+02, 0.000000000E+00; 49P0000025 116,-0.289564648E+02, 0.178523273E+02, 0.000000000E+00; 51P0000026 116,-0.284564095E+02, 0.175238132E+02, 0.000000000E+00; 53P0000027 116,-0.279463978E+02, 0.172108078E+02, 0.000000000E+00; 55P0000028 116,-0.274269428E+02, 0.169135609E+02, 0.000000000E+00; 57P0000029 116,-0.268985901E+02, 0.166322689E+02, 0.000000000E+00; 59P0000030 116,-0.263618164E+02, 0.163672466E+02, 0.000000000E+00; 61P0000031 116,-0.258168755E+02, 0.161193409E+02, 0.000000000E+00; 63P0000032 116,-0.252644215E+02, 0.158886490E+02, 0.000000000E+00; 65P0000033 116,-0.247067204E+02, 0.156738577E+02, 0.000000000E+00; 67P0000034 116,-0.241937656E+02, 0.154889746E+02, 0.000000000E+00; 69P0000035


UNCLASSIFIED 82

116,-0.236814594E+02, 0.153152571E+02, 0.000000000E+00; 71P0000036 116,-0.231680965E+02, 0.151513481E+02, 0.000000000E+00; 73P0000037 116,-0.226541939E+02, 0.149961777E+02, 0.000000000E+00; 75P0000038 116,-0.221392269E+02, 0.148486605E+02, 0.000000000E+00; 77P0000039 116,-0.216237564E+02, 0.147083998E+02, 0.000000000E+00; 79P0000040 116,-0.211072311E+02, 0.145748158E+02, 0.000000000E+00; 81P0000041 116,-0.205900307E+02, 0.144476175E+02, 0.000000000E+00; 83P0000042 116,-0.200719299E+02, 0.143264122E+02, 0.000000000E+00; 85P0000043 116,-0.195530891E+02, 0.142109079E+02, 0.000000000E+00; 87P0000044 116,-0.190334587E+02, 0.141008053E+02, 0.000000000E+00; 89P0000045 116,-0.185130539E+02, 0.139958887E+02, 0.000000000E+00; 91P0000046 116,-0.179918289E+02, 0.138959665E+02, 0.000000000E+00; 93P0000047 116,-0.174698811E+02, 0.138008032E+02, 0.000000000E+00; 95P0000048 116,-0.169472923E+02, 0.137101908E+02, 0.000000000E+00; 97P0000049 116,-0.164240055E+02, 0.136239529E+02, 0.000000000E+00; 99P0000050 116,-0.159001150E+02, 0.135419436E+02, 0.000000000E+00; 101P0000051 116,-0.153755722E+02, 0.134640064E+02, 0.000000000E+00; 103P0000052 116,-0.148504686E+02, 0.133900042E+02, 0.000000000E+00; 105P0000053 116,-0.143248320E+02, 0.133197947E+02, 0.000000000E+00; 107P0000054 116,-0.137986803E+02, 0.132532358E+02, 0.000000000E+00; 109P0000055 116,-0.132720242E+02, 0.131902113E+02, 0.000000000E+00; 111P0000056 116,-0.127448997E+02, 0.131306105E+02, 0.000000000E+00; 113P0000057 116,-0.122173347E+02, 0.130743256E+02, 0.000000000E+00; 115P0000058 116,-0.116893616E+02, 0.130212660E+02, 0.000000000E+00; 117P0000059 116,-0.111609440E+02, 0.129712944E+02, 0.000000000E+00; 119P0000060 116,-0.106321650E+02, 0.129243021E+02, 0.000000000E+00; 121P0000061 116,-0.101029987E+02, 0.128802071E+02, 0.000000000E+00; 123P0000062 116,-0.957347870E+01, 0.128389349E+02, 0.000000000E+00; 125P0000063 116,-0.904359055E+01, 0.128003855E+02, 0.000000000E+00; 127P0000064 116,-0.851331615E+01, 0.127644567E+02, 0.000000000E+00; 129P0000065 116,-0.798270082E+01, 0.127310963E+02, 0.000000000E+00; 131P0000066 116,-0.745158482E+01, 0.127002268E+02, 0.000000000E+00; 133P0000067 116,-0.692006493E+01, 0.126717653E+02, 0.000000000E+00; 135P0000068 116,-0.638768721E+01, 0.126455956E+02, 0.000000000E+00; 137P0000069 116,-0.585458183E+01, 0.126217184E+02, 0.000000000E+00; 139P0000070 116,-0.531466722E+01, 0.125998888E+02, 0.000000000E+00; 141P0000071 116,-0.477596521E+01, 0.125803833E+02, 0.000000000E+00; 143P0000072 116,-0.423972416E+01, 0.125631456E+02, 0.000000000E+00; 145P0000073 116,-0.370539904E+01, 0.125481033E+02, 0.000000000E+00; 147P0000074 116,-0.317296505E+01, 0.125352087E+02, 0.000000000E+00; 149P0000075 116,-0.264191699E+01, 0.125243893E+02, 0.000000000E+00; 151P0000076 116,-0.211211109E+01, 0.125155840E+02, 0.000000000E+00; 153P0000077 116,-0.158315206E+01, 0.125087614E+02, 0.000000000E+00; 155P0000078 116,-0.105489695E+01, 0.125038977E+02, 0.000000000E+00; 157P0000079 116,-0.526956022E+00, 0.125009747E+02, 0.000000000E+00; 159P0000080 116, 0.000000000E+00, 0.125000000E+02, 0.000000000E+00; 161P0000081 116, 0.526956022E+00, 0.125009747E+02, 0.000000000E+00; 163P0000082 116, 0.105489695E+01, 0.125038977E+02, 0.000000000E+00; 165P0000083 116, 0.158315206E+01, 0.125087614E+02, 0.000000000E+00; 167P0000084 116, 0.211211109E+01, 0.125155840E+02, 0.000000000E+00; 169P0000085 116, 0.264191699E+01, 0.125243893E+02, 0.000000000E+00; 171P0000086 116, 0.317296505E+01, 0.125352087E+02, 0.000000000E+00; 173P0000087 116, 0.370539904E+01, 0.125481033E+02, 0.000000000E+00; 175P0000088 116, 0.423972416E+01, 0.125631456E+02, 0.000000000E+00; 177P0000089 116, 0.477596521E+01, 0.125803833E+02, 0.000000000E+00; 179P0000090 116, 0.531466722E+01, 0.125998888E+02, 0.000000000E+00; 181P0000091 116, 0.585458183E+01, 0.126217184E+02, 0.000000000E+00; 183P0000092 116, 0.638768721E+01, 0.126455956E+02, 0.000000000E+00; 185P0000093 116, 0.692006493E+01, 0.126717653E+02, 0.000000000E+00; 187P0000094 116, 0.745158482E+01, 0.127002268E+02, 0.000000000E+00; 189P0000095


UNCLASSIFIED 83

116, 0.798270082E+01, 0.127310963E+02, 0.000000000E+00; 191P0000096 116, 0.851331615E+01, 0.127644567E+02, 0.000000000E+00; 193P0000097 116, 0.904359055E+01, 0.128003855E+02, 0.000000000E+00; 195P0000098 116, 0.957347870E+01, 0.128389349E+02, 0.000000000E+00; 197P0000099 116, 0.101029987E+02, 0.128802071E+02, 0.000000000E+00; 199P0000100 116, 0.106321650E+02, 0.129243021E+02, 0.000000000E+00; 201P0000101 116, 0.111609440E+02, 0.129712944E+02, 0.000000000E+00; 203P0000102 116, 0.116893616E+02, 0.130212660E+02, 0.000000000E+00; 205P0000103 116, 0.122173347E+02, 0.130743256E+02, 0.000000000E+00; 207P0000104 116, 0.127448997E+02, 0.131306105E+02, 0.000000000E+00; 209P0000105 116, 0.132720242E+02, 0.131902113E+02, 0.000000000E+00; 211P0000106 116, 0.137986803E+02, 0.132532358E+02, 0.000000000E+00; 213P0000107 116, 0.143248320E+02, 0.133197947E+02, 0.000000000E+00; 215P0000108 116, 0.148504686E+02, 0.133900042E+02, 0.000000000E+00; 217P0000109 116, 0.153755722E+02, 0.134640064E+02, 0.000000000E+00; 219P0000110 116, 0.159001150E+02, 0.135419436E+02, 0.000000000E+00; 221P0000111 116, 0.164240055E+02, 0.136239529E+02, 0.000000000E+00; 223P0000112 116, 0.169472923E+02, 0.137101908E+02, 0.000000000E+00; 225P0000113 116, 0.174698811E+02, 0.138008032E+02, 0.000000000E+00; 227P0000114 116, 0.179918289E+02, 0.138959665E+02, 0.000000000E+00; 229P0000115 116, 0.185130539E+02, 0.139958887E+02, 0.000000000E+00; 231P0000116 116, 0.190334587E+02, 0.141008053E+02, 0.000000000E+00; 233P0000117 116, 0.195530891E+02, 0.142109079E+02, 0.000000000E+00; 235P0000118 116, 0.200719299E+02, 0.143264122E+02, 0.000000000E+00; 237P0000119 116, 0.205900307E+02, 0.144476175E+02, 0.000000000E+00; 239P0000120 116, 0.211072311E+02, 0.145748158E+02, 0.000000000E+00; 241P0000121 116, 0.216237564E+02, 0.147083998E+02, 0.000000000E+00; 243P0000122 116, 0.221392269E+02, 0.148486605E+02, 0.000000000E+00; 245P0000123 116, 0.226541939E+02, 0.149961777E+02, 0.000000000E+00; 247P0000124 116, 0.231680965E+02, 0.151513481E+02, 0.000000000E+00; 249P0000125 116, 0.236814594E+02, 0.153152571E+02, 0.000000000E+00; 251P0000126 116, 0.241937656E+02, 0.154889746E+02, 0.000000000E+00; 253P0000127 116, 0.247067204E+02, 0.156738577E+02, 0.000000000E+00; 255P0000128 116, 0.252644215E+02, 0.158886490E+02, 0.000000000E+00; 257P0000129 116, 0.258168755E+02, 0.161193409E+02, 0.000000000E+00; 259P0000130 116, 0.263618164E+02, 0.163672466E+02, 0.000000000E+00; 261P0000131 116, 0.268985901E+02, 0.166322689E+02, 0.000000000E+00; 263P0000132 116, 0.274269428E+02, 0.169135609E+02, 0.000000000E+00; 265P0000133 116, 0.279463978E+02, 0.172108078E+02, 0.000000000E+00; 267P0000134 116, 0.284564095E+02, 0.175238132E+02, 0.000000000E+00; 269P0000135 116, 0.289564648E+02, 0.178523273E+02, 0.000000000E+00; 271P0000136 116, 0.294460506E+02, 0.181960793E+02, 0.000000000E+00; 273P0000137 116, 0.299246712E+02, 0.185547771E+02, 0.000000000E+00; 275P0000138 116, 0.303918438E+02, 0.189281139E+02, 0.000000000E+00; 277P0000139 116, 0.308470802E+02, 0.193157578E+02, 0.000000000E+00; 279P0000140 116, 0.312899284E+02, 0.197173615E+02, 0.000000000E+00; 281P0000141 116, 0.317199383E+02, 0.201325626E+02, 0.000000000E+00; 283P0000142 116, 0.321366768E+02, 0.205609684E+02, 0.000000000E+00; 285P0000143 116, 0.325397339E+02, 0.210021782E+02, 0.000000000E+00; 287P0000144 116, 0.329287148E+02, 0.214557743E+02, 0.000000000E+00; 289P0000145 116, 0.333032341E+02, 0.219213123E+02, 0.000000000E+00; 291P0000146 116, 0.336629524E+02, 0.223983402E+02, 0.000000000E+00; 293P0000147 116, 0.340075302E+02, 0.228863926E+02, 0.000000000E+00; 295P0000148 116, 0.343366623E+02, 0.233849792E+02, 0.000000000E+00; 297P0000149 116, 0.346500549E+02, 0.238936100E+02, 0.000000000E+00; 299P0000150 116, 0.349474525E+02, 0.244117718E+02, 0.000000000E+00; 301P0000151 116, 0.352286034E+02, 0.249389458E+02, 0.000000000E+00; 303P0000152 116, 0.354933052E+02, 0.254746056E+02, 0.000000000E+00; 305P0000153 116, 0.357413559E+02, 0.260182152E+02, 0.000000000E+00; 307P0000154 116, 0.359725838E+02, 0.265692329E+02, 0.000000000E+00; 309P0000155


UNCLASSIFIED 84

116, 0.361868477E+02, 0.271271095E+02, 0.000000000E+00; 311P0000156 116, 0.363840218E+02, 0.276912956E+02, 0.000000000E+00; 313P0000157 116, 0.365639954E+02, 0.282612324E+02, 0.000000000E+00; 315P0000158 116, 0.367266922E+02, 0.288363667E+02, 0.000000000E+00; 317P0000159 116, 0.368720512E+02, 0.294161396E+02, 0.000000000E+00; 319P0000160 116, 0.370000000E+02, 0.300000000E+02, 0.000000000E+00; 321P0000161 124,-0.979913771E+00, 0.199421763E+00, 0.000000000E+00, 323P0000162 -0.174294739E+02,-0.199421763E+00,-0.979913771E+00, 323P0000163 0.000000000E+00, 0.339827881E+02, 0.000000000E+00, 323P0000164 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 323P0000165 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 325P0000166 0.199716816E+02, 0.000000000E+00, 0.199627361E+02, 325P0000167 0.597648680E+00; 325P0000168 124,-0.973509073E+00, 0.228648141E+00, 0.000000000E+00, 327P0000169 -0.174294357E+02,-0.228648141E+00,-0.973509073E+00, 327P0000170 0.000000000E+00, 0.339826279E+02, 0.000000000E+00, 327P0000171 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 327P0000172 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 329P0000173 0.199716835E+02, 0.000000000E+00, 0.199627380E+02, 329P0000174 0.597650230E+00; 329P0000175 124,-0.966217399E+00, 0.257728457E+00, 0.000000000E+00, 331P0000176 -0.174903107E+02,-0.257728457E+00,-0.966217399E+00, 331P0000177 0.000000000E+00, 0.339674721E+02, 0.000000000E+00, 331P0000178 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 331P0000179 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 333P0000180 0.199089584E+02, 0.000000000E+00, 0.198999863E+02, 333P0000181 0.597636819E+00; 333P0000182 124,-0.958022058E+00, 0.286694616E+00, 0.000000000E+00, 335P0000183 -0.175956039E+02,-0.286694616E+00,-0.958022058E+00, 335P0000184 0.000000000E+00, 0.339376526E+02, 0.000000000E+00, 335P0000185 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 335P0000186 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 337P0000187 0.197995358E+02, 0.000000000E+00, 0.197905140E+02, 337P0000188 0.597609520E+00; 337P0000189 124,-0.948906660E+00, 0.315557033E+00, 0.000000000E+00, 339P0000190 -0.176932240E+02,-0.315557033E+00,-0.948906660E+00, 339P0000191 0.000000000E+00, 0.339068832E+02, 0.000000000E+00, 339P0000192 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 339P0000193 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 341P0000194 0.196971931E+02, 0.000000000E+00, 0.196881256E+02, 341P0000195 0.597579360E+00; 341P0000196 124,-0.938872039E+00, 0.344266176E+00, 0.000000000E+00, 343P0000197 -0.177804337E+02,-0.344266176E+00,-0.938872039E+00, 343P0000198 0.000000000E+00, 0.338763847E+02, 0.000000000E+00, 343P0000199 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 343P0000200 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 345P0000201 0.196048164E+02, 0.000000000E+00, 0.195957069E+02, 345P0000202 0.597538531E+00; 345P0000203 124,-0.927917957E+00, 0.372784317E+00, 0.000000000E+00, 347P0000204 -0.178656101E+02,-0.372784317E+00,-0.927917957E+00, 347P0000205 0.000000000E+00, 0.338435783E+02, 0.000000000E+00, 347P0000206 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 347P0000207 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 349P0000208 0.195135498E+02, 0.000000000E+00, 0.195044003E+02, 349P0000209 0.597497404E+00; 349P0000210 124,-0.916038990E+00, 0.401089132E+00, 0.000000000E+00, 351P0000211 -0.179434204E+02,-0.401089132E+00,-0.916038990E+00, 351P0000212 0.000000000E+00, 0.338110695E+02, 0.000000000E+00, 351P0000213 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 351P0000214 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 353P0000215


UNCLASSIFIED 85

0.194292336E+02, 0.000000000E+00, 0.194200459E+02, 353P0000216 0.597458005E+00; 353P0000217 124,-0.903244376E+00, 0.429126471E+00, 0.000000000E+00, 355P0000218 -0.180154076E+02,-0.429126471E+00,-0.903244376E+00, 355P0000219 0.000000000E+00, 0.337782593E+02, 0.000000000E+00, 355P0000220 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 355P0000221 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 357P0000222 0.193501320E+02, 0.000000000E+00, 0.193409081E+02, 357P0000223 0.597422302E+00; 357P0000224 124,-0.889543653E+00, 0.456850141E+00, 0.000000000E+00, 359P0000225 -0.180766335E+02,-0.456850141E+00,-0.889543653E+00, 359P0000226 0.000000000E+00, 0.337478218E+02, 0.000000000E+00, 359P0000227 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 359P0000228 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 361P0000229 0.192817631E+02, 0.000000000E+00, 0.192725067E+02, 361P0000230 0.597387969E+00; 361P0000231 124,-0.874933779E+00, 0.484242529E+00, 0.000000000E+00, 363P0000232 -0.181342697E+02,-0.484242529E+00,-0.874933779E+00, 363P0000233 0.000000000E+00, 0.337172279E+02, 0.000000000E+00, 363P0000234 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 363P0000235 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 365P0000236 0.192165203E+02, 0.000000000E+00, 0.192072334E+02, 365P0000237 0.597369611E+00; 365P0000238 124,-0.859439969E+00, 0.511236668E+00, 0.000000000E+00, 367P0000239 -0.181783447E+02,-0.511236668E+00,-0.859439969E+00, 367P0000240 0.000000000E+00, 0.336917839E+02, 0.000000000E+00, 367P0000241 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 367P0000242 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 369P0000243 0.191656322E+02, 0.000000000E+00, 0.191563206E+02, 369P0000244 0.597355425E+00; 369P0000245 124,-0.843064427E+00, 0.537812591E+00, 0.000000000E+00, 371P0000246 -0.182168083E+02,-0.537812591E+00,-0.843064427E+00, 371P0000247 0.000000000E+00, 0.336682510E+02, 0.000000000E+00, 371P0000248 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 371P0000249 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 373P0000250 0.191205482E+02, 0.000000000E+00, 0.191112156E+02, 373P0000251 0.597352207E+00; 373P0000252 124,-0.825838447E+00, 0.563906848E+00, 0.000000000E+00, 375P0000253 -0.182439041E+02,-0.563906848E+00,-0.825838447E+00, 375P0000254 0.000000000E+00, 0.336502609E+02, 0.000000000E+00, 375P0000255 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 375P0000256 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 377P0000257 0.190880260E+02, 0.000000000E+00, 0.190786762E+02, 377P0000258 0.597361743E+00; 377P0000259 124,-0.807771146E+00, 0.589496136E+00, 0.000000000E+00, 379P0000260 -0.182669544E+02,-0.589496136E+00,-0.807771146E+00, 379P0000261 0.000000000E+00, 0.336340485E+02, 0.000000000E+00, 379P0000262 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 379P0000263 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 381P0000264 0.190598507E+02, 0.000000000E+00, 0.190504856E+02, 381P0000265 0.597381592E+00; 381P0000266 124,-0.788896024E+00, 0.614526689E+00, 0.000000000E+00, 383P0000267 -0.182771568E+02,-0.614526689E+00,-0.788896024E+00, 383P0000268 0.000000000E+00, 0.336261826E+02, 0.000000000E+00, 383P0000269 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 383P0000270 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 385P0000271 0.190469685E+02, 0.000000000E+00, 0.190375957E+02, 385P0000272 0.597413361E+00; 385P0000273 124,-0.769225717E+00, 0.638977230E+00, 0.000000000E+00, 387P0000274 -0.182827244E+02,-0.638977230E+00,-0.769225717E+00, 387P0000275


UNCLASSIFIED 86

0.000000000E+00, 0.336218452E+02, 0.000000000E+00, 387P0000276 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 387P0000277 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 389P0000278 0.190399132E+02, 0.000000000E+00, 0.190305367E+02, 389P0000279 0.597467959E+00; 389P0000280 124,-0.748797357E+00, 0.662799001E+00, 0.000000000E+00, 391P0000281 -0.182773380E+02,-0.662799001E+00,-0.748797357E+00, 391P0000282 0.000000000E+00, 0.336265564E+02, 0.000000000E+00, 391P0000283 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 391P0000284 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 393P0000285 0.190470695E+02, 0.000000000E+00, 0.190376949E+02, 393P0000286 0.597521901E+00; 393P0000287 124,-0.727645516E+00, 0.685953319E+00, 0.000000000E+00, 395P0000288 -0.182694244E+02,-0.685953319E+00,-0.727645516E+00, 395P0000289 0.000000000E+00, 0.336336632E+02, 0.000000000E+00, 395P0000290 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 395P0000291 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 397P0000292 0.190577030E+02, 0.000000000E+00, 0.190483322E+02, 397P0000293 0.597590744E+00; 397P0000294 124,-0.705793202E+00, 0.708417952E+00, 0.000000000E+00, 399P0000295 -0.182517509E+02,-0.708417952E+00,-0.705793202E+00, 399P0000296 0.000000000E+00, 0.336508369E+02, 0.000000000E+00, 399P0000297 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 399P0000298 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 401P0000299 0.190823421E+02, 0.000000000E+00, 0.190729809E+02, 401P0000300 0.597673297E+00; 401P0000301 124,-0.683273613E+00, 0.730162323E+00, 0.000000000E+00, 403P0000302 -0.182318077E+02,-0.730162323E+00,-0.683273613E+00, 403P0000303 0.000000000E+00, 0.336715775E+02, 0.000000000E+00, 403P0000304 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 403P0000305 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 405P0000306 0.191111145E+02, 0.000000000E+00, 0.191017628E+02, 405P0000307 0.597756207E+00; 405P0000308 124,-0.660127938E+00, 0.751153171E+00, 0.000000000E+00, 407P0000309 -0.182056084E+02,-0.751153171E+00,-0.660127938E+00, 407P0000310 0.000000000E+00, 0.337003670E+02, 0.000000000E+00, 407P0000311 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 407P0000312 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 409P0000313 0.191500340E+02, 0.000000000E+00, 0.191406994E+02, 409P0000314 0.597847521E+00; 409P0000315 124,-0.636380374E+00, 0.771375477E+00, 0.000000000E+00, 411P0000316 -0.181777573E+02,-0.771375477E+00,-0.636380374E+00, 411P0000317 0.000000000E+00, 0.337331696E+02, 0.000000000E+00, 411P0000318 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 411P0000319 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 413P0000320 0.191930599E+02, 0.000000000E+00, 0.191837425E+02, 413P0000321 0.597949684E+00; 413P0000322 124,-0.612075329E+00, 0.790799439E+00, 0.000000000E+00, 415P0000323 -0.181443787E+02,-0.790799439E+00,-0.612075329E+00, 415P0000324 0.000000000E+00, 0.337748795E+02, 0.000000000E+00, 415P0000325 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 415P0000326 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 417P0000327 0.192464752E+02, 0.000000000E+00, 0.192371826E+02, 417P0000328 0.598043382E+00; 417P0000329 124,-0.587244272E+00, 0.809409797E+00, 0.000000000E+00, 419P0000330 -0.181114426E+02,-0.809409797E+00,-0.587244272E+00, 419P0000331 0.000000000E+00, 0.338187828E+02, 0.000000000E+00, 419P0000332 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 419P0000333 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 421P0000334 0.193013515E+02, 0.000000000E+00, 0.192920818E+02, 421P0000335


UNCLASSIFIED 87

0.598142266E+00; 421P0000336 124,-0.561916232E+00, 0.827194095E+00, 0.000000000E+00, 423P0000337 -0.180766201E+02,-0.827194095E+00,-0.561916232E+00, 423P0000338 0.000000000E+00, 0.338684921E+02, 0.000000000E+00, 423P0000339 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 423P0000340 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 425P0000341 0.193620396E+02, 0.000000000E+00, 0.193527946E+02, 425P0000342 0.598239958E+00; 425P0000343 124,-0.536134243E+00, 0.844132781E+00, 0.000000000E+00, 427P0000344 -0.180413818E+02,-0.844132781E+00,-0.536134243E+00, 427P0000345 0.000000000E+00, 0.339220695E+02, 0.000000000E+00, 427P0000346 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 427P0000347 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 429P0000348 0.194261570E+02, 0.000000000E+00, 0.194169407E+02, 429P0000349 0.598330975E+00; 429P0000350 124,-0.509926081E+00, 0.860218167E+00, 0.000000000E+00, 431P0000351 -0.180050697E+02,-0.860218167E+00,-0.509926081E+00, 431P0000352 0.000000000E+00, 0.339813004E+02, 0.000000000E+00, 431P0000353 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 431P0000354 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 433P0000355 0.194956264E+02, 0.000000000E+00, 0.194864407E+02, 433P0000356 0.598419130E+00; 433P0000357 124,-0.483360291E+00, 0.875421464E+00, 0.000000000E+00, 435P0000358 -0.179487839E+02,-0.875421464E+00,-0.483360291E+00, 435P0000359 0.000000000E+00, 0.340796051E+02, 0.000000000E+00, 435P0000360 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 435P0000361 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 437P0000362 0.196088905E+02, 0.000000000E+00, 0.195997562E+02, 437P0000363 0.598497033E+00; 437P0000364 124,-0.456381410E+00, 0.889784276E+00, 0.000000000E+00, 439P0000365 -0.179720745E+02,-0.889784276E+00,-0.456381410E+00, 439P0000366 0.000000000E+00, 0.340358543E+02, 0.000000000E+00, 439P0000367 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 439P0000368 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 441P0000369 0.195593319E+02, 0.000000000E+00, 0.195501709E+02, 441P0000370 0.598563671E+00; 441P0000371 124,-0.428454041E+00, 0.903563619E+00, 0.000000000E+00, 443P0000372 -0.182654037E+02,-0.903563619E+00,-0.428454041E+00, 443P0000373 0.000000000E+00, 0.334417114E+02, 0.000000000E+00, 443P0000374 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 443P0000375 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 445P0000376 0.188968048E+02, 0.000000000E+00, 0.188873215E+02, 445P0000377 0.598604500E+00; 445P0000378 124,-0.399757802E+00, 0.916620851E+00, 0.000000000E+00, 447P0000379 -0.181879711E+02,-0.916620851E+00,-0.399757802E+00, 447P0000380 0.000000000E+00, 0.336119652E+02, 0.000000000E+00, 447P0000381 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 447P0000382 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 449P0000383 0.190838165E+02, 0.000000000E+00, 0.190744247E+02, 449P0000384 0.598612010E+00; 449P0000385 124,-0.372391552E+00, 0.928075731E+00, 0.000000000E+00, 451P0000386 -0.172910404E+02,-0.928075731E+00,-0.372391552E+00, 451P0000387 0.000000000E+00, 0.357599411E+02, 0.000000000E+00, 451P0000388 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 451P0000389 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 453P0000390 0.214112835E+02, 0.000000000E+00, 0.214029427E+02, 453P0000391 0.597575188E+00; 453P0000392 124,-0.348794401E+00, 0.937199295E+00, 0.000000000E+00, 455P0000393 -0.155191765E+02,-0.937199295E+00,-0.348794401E+00, 455P0000394 0.000000000E+00, 0.403604927E+02, 0.000000000E+00, 455P0000395


UNCLASSIFIED 88

0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 455P0000396 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 457P0000397 0.263408585E+02, 0.000000000E+00, 0.263352165E+02, 457P0000398 0.545227349E+00; 457P0000399 124,-0.330081433E+00, 0.943952441E+00, 0.000000000E+00, 459P0000400 -0.147639360E+02,-0.943952441E+00,-0.330081433E+00, 459P0000401 0.000000000E+00, 0.424559898E+02, 0.000000000E+00, 459P0000402 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 459P0000403 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 461P0000404 0.285681915E+02, 0.000000000E+00, 0.285630703E+02, 461P0000405 0.540933967E+00; 461P0000406 124,-0.312640846E+00, 0.949871421E+00, 0.000000000E+00, 463P0000407 -0.142351799E+02,-0.949871421E+00,-0.312640846E+00, 463P0000408 0.000000000E+00, 0.440151253E+02, 0.000000000E+00, 463P0000409 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 463P0000410 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 465P0000411 0.302144756E+02, 0.000000000E+00, 0.302096691E+02, 465P0000412 0.538873434E+00; 465P0000413 124,-0.296600670E+00, 0.955001593E+00, 0.000000000E+00, 467P0000414 -0.130788708E+02,-0.955001593E+00,-0.296600670E+00, 467P0000415 0.000000000E+00, 0.476368675E+02, 0.000000000E+00, 467P0000416 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 467P0000417 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 469P0000418 0.340161934E+02, 0.000000000E+00, 0.340119591E+02, 469P0000419 0.536801577E+00; 469P0000420 124,-0.282218993E+00, 0.959350049E+00, 0.000000000E+00, 471P0000421 -0.120343409E+02,-0.959350049E+00,-0.282218993E+00, 471P0000422 0.000000000E+00, 0.510963554E+02, 0.000000000E+00, 471P0000423 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 471P0000424 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 473P0000425 0.376298294E+02, 0.000000000E+00, 0.376260147E+02, 473P0000426 0.535665035E+00; 473P0000427 124,-0.268968552E+00, 0.963148952E+00, 0.000000000E+00, 475P0000428 -0.113384686E+02,-0.963148952E+00,-0.268968552E+00, 475P0000429 0.000000000E+00, 0.535250740E+02, 0.000000000E+00, 475P0000430 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 475P0000431 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 477P0000432 0.401562119E+02, 0.000000000E+00, 0.401526566E+02, 477P0000433 0.534200490E+00; 477P0000434 124,-0.256469101E+00, 0.966552377E+00, 0.000000000E+00, 479P0000435 -0.107500238E+02,-0.966552377E+00,-0.256469101E+00, 479P0000436 0.000000000E+00, 0.556881218E+02, 0.000000000E+00, 479P0000437 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 479P0000438 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 481P0000439 0.423978271E+02, 0.000000000E+00, 0.423944702E+02, 481P0000440 0.533509314E+00; 481P0000441 124,-0.244601488E+00, 0.969623744E+00, 0.000000000E+00, 483P0000442 -0.101752138E+02,-0.969623744E+00,-0.244601488E+00, 483P0000443 0.000000000E+00, 0.579103775E+02, 0.000000000E+00, 483P0000444 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 483P0000445 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 485P0000446 0.446931763E+02, 0.000000000E+00, 0.446900024E+02, 485P0000447 0.532602072E+00; 485P0000448 124,-0.233305708E+00, 0.972403407E+00, 0.000000000E+00, 487P0000449 -0.963730145E+01,-0.972403407E+00,-0.233305708E+00, 487P0000450 0.000000000E+00, 0.600979004E+02, 0.000000000E+00, 487P0000451 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 487P0000452 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 489P0000453 0.469458275E+02, 0.000000000E+00, 0.469428101E+02, 489P0000454 0.532081127E+00; 489P0000455


UNCLASSIFIED 89

124,-0.222546503E+00, 0.974922061E+00, 0.000000000E+00, 491P0000456 -0.907370281E+01,-0.974922061E+00,-0.222546503E+00, 491P0000457 0.000000000E+00, 0.625069695E+02, 0.000000000E+00, 491P0000458 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 491P0000459 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 493P0000460 0.494199066E+02, 0.000000000E+00, 0.494170494E+02, 493P0000461 0.531534672E+00; 493P0000462 124,-0.212293595E+00, 0.977205932E+00, 0.000000000E+00, 495P0000463 -0.854782581E+01,-0.977205932E+00,-0.212293595E+00, 495P0000464 0.000000000E+00, 0.648690948E+02, 0.000000000E+00, 495P0000465 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 495P0000466 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 497P0000467 0.518398285E+02, 0.000000000E+00, 0.518371048E+02, 497P0000468 0.531160057E+00; 497P0000469 124,-0.202458948E+00, 0.979290724E+00, 0.000000000E+00, 499P0000470 -0.813101196E+01,-0.979290724E+00,-0.202458948E+00, 499P0000471 0.000000000E+00, 0.668357697E+02, 0.000000000E+00, 499P0000472 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 499P0000473 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 501P0000474 0.538501587E+02, 0.000000000E+00, 0.538475418E+02, 501P0000475 0.530869424E+00; 501P0000476 124,-0.192953706E+00, 0.981207848E+00, 0.000000000E+00, 503P0000477 -0.776343250E+01,-0.981207848E+00,-0.192953706E+00, 503P0000478 0.000000000E+00, 0.686598434E+02, 0.000000000E+00, 503P0000479 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 503P0000480 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 505P0000481 0.557108841E+02, 0.000000000E+00, 0.557083588E+02, 505P0000482 0.530710220E+00; 505P0000483 124,-0.183823273E+00, 0.982959330E+00, 0.000000000E+00, 507P0000484 -0.723191309E+01,-0.982959330E+00,-0.183823273E+00, 507P0000485 0.000000000E+00, 0.714325333E+02, 0.000000000E+00, 507P0000486 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 507P0000487 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 509P0000488 0.585340271E+02, 0.000000000E+00, 0.585316238E+02, 509P0000489 0.530547082E+00; 509P0000490 124,-0.175106868E+00, 0.984549463E+00, 0.000000000E+00, 511P0000491 -0.674493647E+01,-0.984549463E+00,-0.175106868E+00, 511P0000492 0.000000000E+00, 0.741024857E+02, 0.000000000E+00, 511P0000493 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 511P0000494 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 513P0000495 0.612479973E+02, 0.000000000E+00, 0.612457008E+02, 513P0000496 0.530381560E+00; 513P0000497 124,-0.166724965E+00, 0.986003399E+00, 0.000000000E+00, 515P0000498 -0.635743904E+01,-0.986003399E+00,-0.166724965E+00, 515P0000499 0.000000000E+00, 0.763380737E+02, 0.000000000E+00, 515P0000500 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 515P0000501 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 517P0000502 0.635169029E+02, 0.000000000E+00, 0.635146866E+02, 517P0000503 0.530340910E+00; 517P0000504 124,-0.158633173E+00, 0.987337589E+00, 0.000000000E+00, 519P0000505 -0.598036671E+01,-0.987337589E+00,-0.158633173E+00, 519P0000506 0.000000000E+00, 0.786254730E+02, 0.000000000E+00, 519P0000507 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 519P0000508 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 521P0000509 0.658351517E+02, 0.000000000E+00, 0.658330154E+02, 521P0000510 0.530266404E+00; 521P0000511 124,-0.150810868E+00, 0.988562703E+00, 0.000000000E+00, 523P0000512 -0.561133671E+01,-0.988562703E+00,-0.150810868E+00, 523P0000513 0.000000000E+00, 0.809847107E+02, 0.000000000E+00, 523P0000514 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 523P0000515


UNCLASSIFIED 90

100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 525P0000516 0.682230530E+02, 0.000000000E+00, 0.682209930E+02, 525P0000517 0.530296922E+00; 525P0000518 124,-0.143262208E+00, 0.989684820E+00, 0.000000000E+00, 527P0000519 -0.524605465E+01,-0.989684820E+00,-0.143262208E+00, 527P0000520 0.000000000E+00, 0.834407959E+02, 0.000000000E+00, 527P0000521 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 527P0000522 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 529P0000523 0.707061386E+02, 0.000000000E+00, 0.707041473E+02, 529P0000524 0.530288279E+00; 529P0000525 124,-0.135972485E+00, 0.990712643E+00, 0.000000000E+00, 531P0000526 -0.486481571E+01,-0.990712643E+00,-0.135972485E+00, 531P0000527 0.000000000E+00, 0.861467285E+02, 0.000000000E+00, 531P0000528 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 531P0000529 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 533P0000530 0.734387741E+02, 0.000000000E+00, 0.734368591E+02, 533P0000531 0.530301392E+00; 533P0000532 124,-0.128948435E+00, 0.991651297E+00, 0.000000000E+00, 535P0000533 -0.448669863E+01,-0.991651297E+00,-0.128948435E+00, 535P0000534 0.000000000E+00, 0.889779282E+02, 0.000000000E+00, 535P0000535 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 535P0000536 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 537P0000537 0.762950974E+02, 0.000000000E+00, 0.762932587E+02, 537P0000538 0.530341923E+00; 537P0000539 124,-0.122161500E+00, 0.992510200E+00, 0.000000000E+00, 539P0000540 -0.416952467E+01,-0.992510200E+00,-0.122161500E+00, 539P0000541 0.000000000E+00, 0.914860306E+02, 0.000000000E+00, 539P0000542 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 539P0000543 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 541P0000544 0.788231659E+02, 0.000000000E+00, 0.788213806E+02, 541P0000545 0.530411243E+00; 541P0000546 124,-0.115587756E+00, 0.993297279E+00, 0.000000000E+00, 543P0000547 -0.385886765E+01,-0.993297279E+00,-0.115587756E+00, 543P0000548 0.000000000E+00, 0.940816727E+02, 0.000000000E+00, 543P0000549 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 543P0000550 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 545P0000551 0.814373169E+02, 0.000000000E+00, 0.814355927E+02, 545P0000552 0.530480146E+00; 545P0000553 124,-0.109221675E+00, 0.994017422E+00, 0.000000000E+00, 547P0000554 -0.355825663E+01,-0.994017422E+00,-0.109221675E+00, 547P0000555 0.000000000E+00, 0.967374878E+02, 0.000000000E+00, 547P0000556 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 547P0000557 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 549P0000558 0.841100769E+02, 0.000000000E+00, 0.841084061E+02, 549P0000559 0.530556202E+00; 549P0000560 124,-0.103037842E+00, 0.994677424E+00, 0.000000000E+00, 551P0000561 -0.328518891E+01,-0.994677424E+00,-0.103037842E+00, 551P0000562 0.000000000E+00, 0.993009415E+02, 0.000000000E+00, 551P0000563 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 551P0000564 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 553P0000565 0.866880188E+02, 0.000000000E+00, 0.866863937E+02, 553P0000566 0.530630708E+00; 553P0000567 124,-0.970726684E-01, 0.995277345E+00, 0.000000000E+00, 555P0000568 -0.292032695E+01,-0.995277345E+00,-0.970726684E-01, 555P0000569 0.000000000E+00, 0.102929382E+03, 0.000000000E+00, 555P0000570 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 555P0000571 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 557P0000572 0.903347397E+02, 0.000000000E+00, 0.903331757E+02, 557P0000573 0.530772209E+00; 557P0000574 124,-0.913348272E-01, 0.995820284E+00, 0.000000000E+00, 559P0000575


UNCLASSIFIED 91

-0.258141685E+01,-0.995820284E+00,-0.913348272E-01, 559P0000576 0.000000000E+00, 0.106513557E+03, 0.000000000E+00, 559P0000577 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 559P0000578 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 561P0000579 0.939348907E+02, 0.000000000E+00, 0.939333878E+02, 561P0000580 0.530860126E+00; 561P0000581 124,-0.857818872E-01, 0.996313930E+00, 0.000000000E+00, 563P0000582 -0.235100842E+01,-0.996313930E+00,-0.857818872E-01, 563P0000583 0.000000000E+00, 0.109105812E+03, 0.000000000E+00, 563P0000584 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 563P0000585 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 565P0000586 0.965373535E+02, 0.000000000E+00, 0.965358887E+02, 565P0000587 0.530998051E+00; 565P0000588 124,-0.803748369E-01, 0.996764719E+00, 0.000000000E+00, 567P0000589 -0.212761569E+01,-0.996764719E+00,-0.803748369E-01, 567P0000590 0.000000000E+00, 0.111786530E+03, 0.000000000E+00, 567P0000591 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 567P0000592 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 569P0000593 0.992273560E+02, 0.000000000E+00, 0.992259369E+02, 569P0000594 0.531123221E+00; 569P0000595 124,-0.751318336E-01, 0.997173607E+00, 0.000000000E+00, 571P0000596 -0.183925605E+01,-0.997173607E+00,-0.751318336E-01, 571P0000597 0.000000000E+00, 0.115489998E+03, 0.000000000E+00, 571P0000598 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 571P0000599 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 573P0000600 0.102942017E+03, 0.000000000E+00, 0.102940651E+03, 573P0000601 0.531286657E+00; 573P0000602 124,-0.700825006E-01, 0.997541189E+00, 0.000000000E+00, 575P0000603 -0.155930030E+01,-0.997541189E+00,-0.700825006E-01, 575P0000604 0.000000000E+00, 0.119330376E+03, 0.000000000E+00, 575P0000605 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 575P0000606 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 577P0000607 0.106792572E+03, 0.000000000E+00, 0.106791245E+03, 577P0000608 0.531488895E+00; 577P0000609 124,-0.651721880E-01, 0.997874022E+00, 0.000000000E+00, 579P0000610 -0.138299394E+01,-0.997874022E+00,-0.651721880E-01, 579P0000611 0.000000000E+00, 0.121939308E+03, 0.000000000E+00, 579P0000612 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 579P0000613 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 581P0000614 0.109407448E+03, 0.000000000E+00, 0.109406158E+03, 581P0000615 0.531662047E+00; 581P0000616 124,-0.603878759E-01, 0.998174965E+00, 0.000000000E+00, 583P0000617 -0.119919837E+01,-0.998174965E+00,-0.603878759E-01, 583P0000618 0.000000000E+00, 0.124858276E+03, 0.000000000E+00, 583P0000619 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 583P0000620 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 585P0000621 0.112332191E+03, 0.000000000E+00, 0.112330933E+03, 585P0000622 0.532010794E+00; 585P0000623 124,-0.557466447E-01, 0.998444915E+00, 0.000000000E+00, 587P0000624 -0.942494392E+00,-0.998444915E+00,-0.557466447E-01, 587P0000625 0.000000000E+00, 0.129280670E+03, 0.000000000E+00, 587P0000626 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 587P0000627 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 589P0000628 0.116762016E+03, 0.000000000E+00, 0.116760803E+03, 589P0000629 0.532280326E+00; 589P0000630 124,-0.512870625E-01, 0.998683929E+00, 0.000000000E+00, 591P0000631 -0.686398745E+00,-0.998683929E+00,-0.512870625E-01, 591P0000632 0.000000000E+00, 0.134056427E+03, 0.000000000E+00, 591P0000633 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 591P0000634 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 593P0000635


UNCLASSIFIED 92

0.121544617E+03, 0.000000000E+00, 0.121543449E+03, 593P0000636 0.533019722E+00; 593P0000637 124,-0.469208211E-01, 0.998898566E+00, 0.000000000E+00, 595P0000638 -0.642672896E+00,-0.998898566E+00,-0.469208211E-01, 595P0000639 0.000000000E+00, 0.134951355E+03, 0.000000000E+00, 595P0000640 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 595P0000641 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 597P0000642 0.122440613E+03, 0.000000000E+00, 0.122439453E+03, 597P0000643 0.533638656E+00; 597P0000644 124,-0.425853617E-01, 0.999092817E+00, 0.000000000E+00, 599P0000645 -0.597664952E+00,-0.999092817E+00,-0.425853617E-01, 599P0000646 0.000000000E+00, 0.135953964E+03, 0.000000000E+00, 599P0000647 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 599P0000648 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 601P0000649 0.123444229E+03, 0.000000000E+00, 0.123443047E+03, 601P0000650 0.540354848E+00; 601P0000651 124,-0.382892787E-01, 0.999266684E+00, 0.000000000E+00, 603P0000652 -0.414655149E+00,-0.999266684E+00,-0.382892787E-01, 603P0000653 0.000000000E+00, 0.140479523E+03, 0.000000000E+00, 603P0000654 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 603P0000655 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 605P0000656 0.127973473E+03, 0.000000000E+00, 0.127972336E+03, 605P0000657 0.539053917E+00; 605P0000658 124,-0.341517664E-01, 0.999416590E+00, 0.000000000E+00, 607P0000659 -0.249782860E+00,-0.999416590E+00,-0.341517664E-01, 607P0000660 0.000000000E+00, 0.145034485E+03, 0.000000000E+00, 607P0000661 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 607P0000662 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 609P0000663 0.132531418E+03, 0.000000000E+00, 0.132530334E+03, 609P0000664 0.536516726E+00; 609P0000665 124,-0.301309396E-01, 0.999545991E+00, 0.000000000E+00, 611P0000666 -0.194920644E+00,-0.999545991E+00,-0.301309396E-01, 611P0000667 0.000000000E+00, 0.146743073E+03, 0.000000000E+00, 611P0000668 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 611P0000669 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 613P0000670 0.134240875E+03, 0.000000000E+00, 0.134239807E+03, 613P0000671 0.534535766E+00; 613P0000672 124,-0.261738934E-01, 0.999657452E+00, 0.000000000E+00, 615P0000673 -0.155343801E+00,-0.999657452E+00,-0.261738934E-01, 615P0000674 0.000000000E+00, 0.148135086E+03, 0.000000000E+00, 615P0000675 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 615P0000676 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 617P0000677 0.135633438E+03, 0.000000000E+00, 0.135632401E+03, 617P0000678 0.532589018E+00; 617P0000679 124,-0.222854689E-01, 0.999751627E+00, 0.000000000E+00, 619P0000680 -0.845837668E-01,-0.999751627E+00,-0.222854689E-01, 619P0000681 0.000000000E+00, 0.151083511E+03, 0.000000000E+00, 619P0000682 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 619P0000683 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 621P0000684 0.138582733E+03, 0.000000000E+00, 0.138581711E+03, 621P0000685 0.531157017E+00; 621P0000686 124,-0.184925944E-01, 0.999828994E+00, 0.000000000E+00, 623P0000687 -0.293985233E-01,-0.999828994E+00,-0.184925944E-01, 623P0000688 0.000000000E+00, 0.153774002E+03, 0.000000000E+00, 623P0000689 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 623P0000690 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 625P0000691 0.141273773E+03, 0.000000000E+00, 0.141272781E+03, 625P0000692 0.529878199E+00; 625P0000693 124,-0.147552537E-01, 0.999891162E+00, 0.000000000E+00, 627P0000694 -0.119952122E-01,-0.999891162E+00,-0.147552537E-01, 627P0000695


UNCLASSIFIED 93

0.000000000E+00, 0.154830124E+03, 0.000000000E+00, 627P0000696 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 627P0000697 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 629P0000698 0.142330032E+03, 0.000000000E+00, 0.142329056E+03, 629P0000699 0.529001892E+00; 629P0000700 124,-0.110523878E-01, 0.999938905E+00, 0.000000000E+00, 631P0000701 -0.143608858E-02,-0.999938905E+00,-0.110523878E-01, 631P0000702 0.000000000E+00, 0.155610809E+03, 0.000000000E+00, 631P0000703 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 631P0000704 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 633P0000705 0.143110794E+03, 0.000000000E+00, 0.143109818E+03, 633P0000706 0.528276563E+00; 633P0000707 124,-0.736975716E-02, 0.999972880E+00, 0.000000000E+00, 635P0000708 0.629189005E-02,-0.999972880E+00,-0.736975716E-02, 635P0000709 0.000000000E+00, 0.156492355E+03, 0.000000000E+00, 635P0000710 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 635P0000711 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 637P0000712 0.143992371E+03, 0.000000000E+00, 0.143991394E+03, 637P0000713 0.527948081E+00; 637P0000714 124,-0.369096897E-02, 0.999993145E+00, 0.000000000E+00, 639P0000715 0.117449241E-02,-0.999993145E+00,-0.369096897E-02, 639P0000716 0.000000000E+00, 0.155587234E+03, 0.000000000E+00, 639P0000717 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 639P0000718 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 641P0000719 0.143087234E+03, 0.000000000E+00, 0.143086258E+03, 641P0000720 0.526956081E+00; 641P0000721 124,-0.869870917E-06, 0.100000000E+01, 0.000000000E+00, 643P0000722 0.123856807E-03,-0.100000000E+01,-0.869870917E-06, 643P0000723 0.000000000E+00, 0.154885269E+03, 0.000000000E+00, 643P0000724 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 643P0000725 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 645P0000726 0.142385269E+03, 0.000000000E+00, 0.142384293E+03, 645P0000727 0.526956022E+00; 645P0000728 124, 0.369170983E-02, 0.999993145E+00, 0.000000000E+00, 647P0000729 -0.128045562E-02,-0.999993145E+00, 0.369170983E-02, 647P0000730 0.000000000E+00, 0.155587204E+03, 0.000000000E+00, 647P0000731 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 647P0000732 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 649P0000733 0.143087204E+03, 0.000000000E+00, 0.143086227E+03, 649P0000734 0.527948141E+00; 649P0000735 124, 0.737245614E-02, 0.999972880E+00, 0.000000000E+00, 651P0000736 -0.668047229E-02,-0.999972880E+00, 0.737245614E-02, 651P0000737 0.000000000E+00, 0.156492355E+03, 0.000000000E+00, 651P0000738 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 651P0000739 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 653P0000740 0.143992371E+03, 0.000000000E+00, 0.143991394E+03, 653P0000741 0.528276682E+00; 653P0000742 124, 0.110489652E-01, 0.999938905E+00, 0.000000000E+00, 655P0000743 0.192569825E-02,-0.999938905E+00, 0.110489652E-01, 655P0000744 0.000000000E+00, 0.155610825E+03, 0.000000000E+00, 655P0000745 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 655P0000746 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 657P0000747 0.143110809E+03, 0.000000000E+00, 0.143109833E+03, 657P0000748 0.529002190E+00; 657P0000749 124, 0.147563014E-01, 0.999891102E+00, 0.000000000E+00, 659P0000750 0.118459957E-01,-0.999891102E+00, 0.147563014E-01, 659P0000751 0.000000000E+00, 0.154830124E+03, 0.000000000E+00, 659P0000752 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 659P0000753 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 661P0000754 0.142330048E+03, 0.000000000E+00, 0.142329071E+03, 661P0000755


UNCLASSIFIED 94

0.529878318E+00; 661P0000756 124, 0.184899773E-01, 0.999828994E+00, 0.000000000E+00, 663P0000757 0.297682136E-01,-0.999828994E+00, 0.184899773E-01, 663P0000758 0.000000000E+00, 0.153774002E+03, 0.000000000E+00, 663P0000759 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 663P0000760 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 665P0000761 0.141273773E+03, 0.000000000E+00, 0.141272766E+03, 665P0000762 0.531157374E+00; 665P0000763 124, 0.222901292E-01, 0.999751508E+00, 0.000000000E+00, 667P0000764 0.839382261E-01,-0.999751508E+00, 0.222901292E-01, 667P0000765 0.000000000E+00, 0.151083496E+03, 0.000000000E+00, 667P0000766 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 667P0000767 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 669P0000768 0.138582733E+03, 0.000000000E+00, 0.138581711E+03, 669P0000769 0.532589138E+00; 669P0000770 124, 0.261710249E-01, 0.999657452E+00, 0.000000000E+00, 671P0000771 0.155732855E+00,-0.999657452E+00, 0.261710249E-01, 671P0000772 0.000000000E+00, 0.148135071E+03, 0.000000000E+00, 671P0000773 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 671P0000774 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 673P0000775 0.135633438E+03, 0.000000000E+00, 0.135632385E+03, 673P0000776 0.534536183E+00; 673P0000777 124, 0.301313903E-01, 0.999545872E+00, 0.000000000E+00, 675P0000778 0.194859490E+00,-0.999545872E+00, 0.301313903E-01, 675P0000779 0.000000000E+00, 0.146743073E+03, 0.000000000E+00, 675P0000780 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 675P0000781 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 677P0000782 0.134240891E+03, 0.000000000E+00, 0.134239822E+03, 677P0000783 0.536517084E+00; 677P0000784 124, 0.341521837E-01, 0.999416590E+00, 0.000000000E+00, 679P0000785 0.249728262E+00,-0.999416590E+00, 0.341521837E-01, 679P0000786 0.000000000E+00, 0.145034470E+03, 0.000000000E+00, 679P0000787 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 679P0000788 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 681P0000789 0.132531403E+03, 0.000000000E+00, 0.132530304E+03, 681P0000790 0.539053977E+00; 681P0000791 124, 0.382890143E-01, 0.999266684E+00, 0.000000000E+00, 683P0000792 0.414689153E+00,-0.999266684E+00, 0.382890143E-01, 683P0000793 0.000000000E+00, 0.140479523E+03, 0.000000000E+00, 683P0000794 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 683P0000795 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 685P0000796 0.127973473E+03, 0.000000000E+00, 0.127972328E+03, 685P0000797 0.540354252E+00; 685P0000798 124, 0.425845347E-01, 0.999092877E+00, 0.000000000E+00, 687P0000799 0.597766578E+00,-0.999092877E+00, 0.425845347E-01, 687P0000800 0.000000000E+00, 0.135953979E+03, 0.000000000E+00, 687P0000801 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 687P0000802 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 689P0000803 0.123444237E+03, 0.000000000E+00, 0.123443085E+03, 689P0000804 0.533638239E+00; 689P0000805 124, 0.469229892E-01, 0.998898506E+00, 0.000000000E+00, 691P0000806 0.642408788E+00,-0.998898506E+00, 0.469229892E-01, 691P0000807 0.000000000E+00, 0.134951324E+03, 0.000000000E+00, 691P0000808 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 691P0000809 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 693P0000810 0.122440590E+03, 0.000000000E+00, 0.122439430E+03, 693P0000811 0.533018827E+00; 693P0000812 124, 0.512840487E-01, 0.998684108E+00, 0.000000000E+00, 695P0000813 0.686764121E+00,-0.998684108E+00, 0.512840487E-01, 695P0000814 0.000000000E+00, 0.134056458E+03, 0.000000000E+00, 695P0000815


UNCLASSIFIED 95

0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 695P0000816 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 697P0000817 0.121544632E+03, 0.000000000E+00, 0.121543465E+03, 697P0000818 0.532280087E+00; 697P0000819 124, 0.557494946E-01, 0.998444796E+00, 0.000000000E+00, 699P0000820 0.942161322E+00,-0.998444796E+00, 0.557494946E-01, 699P0000821 0.000000000E+00, 0.129280655E+03, 0.000000000E+00, 699P0000822 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 699P0000823 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 701P0000824 0.116762016E+03, 0.000000000E+00, 0.116760803E+03, 701P0000825 0.532011032E+00; 701P0000826 124, 0.603854246E-01, 0.998175085E+00, 0.000000000E+00, 703P0000827 0.119947362E+01,-0.998175085E+00, 0.603854246E-01, 703P0000828 0.000000000E+00, 0.124858292E+03, 0.000000000E+00, 703P0000829 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 703P0000830 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 705P0000831 0.112332191E+03, 0.000000000E+00, 0.112330933E+03, 705P0000832 0.531661630E+00; 705P0000833 124, 0.651763901E-01, 0.997873724E+00, 0.000000000E+00, 707P0000834 0.138253343E+01,-0.997873724E+00, 0.651763901E-01, 707P0000835 0.000000000E+00, 0.121939285E+03, 0.000000000E+00, 707P0000836 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 707P0000837 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 709P0000838 0.109407455E+03, 0.000000000E+00, 0.109406166E+03, 709P0000839 0.531488121E+00; 709P0000840 124, 0.700772107E-01, 0.997541547E+00, 0.000000000E+00, 711P0000841 0.155986631E+01,-0.997541547E+00, 0.700772107E-01, 711P0000842 0.000000000E+00, 0.119330399E+03, 0.000000000E+00, 711P0000843 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 711P0000844 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 713P0000845 0.106792557E+03, 0.000000000E+00, 0.106791229E+03, 713P0000846 0.531286538E+00; 713P0000847 124, 0.751347169E-01, 0.997173369E+00, 0.000000000E+00, 715P0000848 0.183895874E+01,-0.997173369E+00, 0.751347169E-01, 715P0000849 0.000000000E+00, 0.115489983E+03, 0.000000000E+00, 715P0000850 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 715P0000851 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 717P0000852 0.102942024E+03, 0.000000000E+00, 0.102940659E+03, 717P0000853 0.531124175E+00; 717P0000854 124, 0.803747326E-01, 0.996764719E+00, 0.000000000E+00, 719P0000855 0.212762666E+01,-0.996764719E+00, 0.803747326E-01, 719P0000856 0.000000000E+00, 0.111786530E+03, 0.000000000E+00, 719P0000857 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 719P0000858 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 721P0000859 0.992273560E+02, 0.000000000E+00, 0.992259369E+02, 721P0000860 0.530998647E+00; 721P0000861 124, 0.857815146E-01, 0.996313930E+00, 0.000000000E+00, 723P0000862 0.235104346E+01,-0.996313930E+00, 0.857815146E-01, 723P0000863 0.000000000E+00, 0.109105820E+03, 0.000000000E+00, 723P0000864 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 723P0000865 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 725P0000866 0.965373611E+02, 0.000000000E+00, 0.965358963E+02, 725P0000867 0.530861437E+00; 725P0000868 124, 0.913352370E-01, 0.995820165E+00, 0.000000000E+00, 727P0000869 0.258137846E+01,-0.995820165E+00, 0.913352370E-01, 727P0000870 0.000000000E+00, 0.106513550E+03, 0.000000000E+00, 727P0000871 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 727P0000872 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 729P0000873 0.939348831E+02, 0.000000000E+00, 0.939333801E+02, 729P0000874 0.530773342E+00; 729P0000875


UNCLASSIFIED 96

124, 0.970703065E-01, 0.995277524E+00, 0.000000000E+00, 731P0000876 0.292054009E+01,-0.995277524E+00, 0.970703065E-01, 731P0000877 0.000000000E+00, 0.102929405E+03, 0.000000000E+00, 731P0000878 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 731P0000879 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 733P0000880 0.903347473E+02, 0.000000000E+00, 0.903331909E+02, 733P0000881 0.530630648E+00; 733P0000882 124, 0.103042655E+00, 0.994676888E+00, 0.000000000E+00, 735P0000883 0.328477216E+01,-0.994676888E+00, 0.103042655E+00, 735P0000884 0.000000000E+00, 0.993008881E+02, 0.000000000E+00, 735P0000885 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 735P0000886 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 737P0000887 0.866880112E+02, 0.000000000E+00, 0.866863861E+02, 737P0000888 0.530556202E+00; 737P0000889 124, 0.109217875E+00, 0.994017839E+00, 0.000000000E+00, 739P0000890 0.355857587E+01,-0.994017839E+00, 0.109217875E+00, 739P0000891 0.000000000E+00, 0.967375259E+02, 0.000000000E+00, 739P0000892 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 739P0000893 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 741P0000894 0.841100769E+02, 0.000000000E+00, 0.841084061E+02, 741P0000895 0.530480742E+00; 741P0000896 124, 0.115587287E+00, 0.993297338E+00, 0.000000000E+00, 743P0000897 0.385890603E+01,-0.993297338E+00, 0.115587287E+00, 743P0000898 0.000000000E+00, 0.940816803E+02, 0.000000000E+00, 743P0000899 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 743P0000900 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 745P0000901 0.814373169E+02, 0.000000000E+00, 0.814355927E+02, 745P0000902 0.530410707E+00; 745P0000903 124, 0.122162804E+00, 0.992510080E+00, 0.000000000E+00, 747P0000904 0.416942215E+01,-0.992510080E+00, 0.122162804E+00, 747P0000905 0.000000000E+00, 0.914860153E+02, 0.000000000E+00, 747P0000906 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 747P0000907 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 749P0000908 0.788231583E+02, 0.000000000E+00, 0.788213730E+02, 749P0000909 0.530341923E+00; 749P0000910 124, 0.128949046E+00, 0.991651237E+00, 0.000000000E+00, 751P0000911 0.448665237E+01,-0.991651237E+00, 0.128949046E+00, 751P0000912 0.000000000E+00, 0.889779205E+02, 0.000000000E+00, 751P0000913 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 751P0000914 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 753P0000915 0.762950974E+02, 0.000000000E+00, 0.762932587E+02, 753P0000916 0.530301511E+00; 753P0000917 124, 0.135973886E+00, 0.990712404E+00, 0.000000000E+00, 755P0000918 0.486471176E+01,-0.990712404E+00, 0.135973886E+00, 755P0000919 0.000000000E+00, 0.861467209E+02, 0.000000000E+00, 755P0000920 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 755P0000921 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 757P0000922 0.734387817E+02, 0.000000000E+00, 0.734368668E+02, 757P0000923 0.530288696E+00; 757P0000924 124, 0.143257305E+00, 0.989685476E+00, 0.000000000E+00, 759P0000925 0.524640179E+01,-0.989685476E+00, 0.143257305E+00, 759P0000926 0.000000000E+00, 0.834408417E+02, 0.000000000E+00, 759P0000927 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 759P0000928 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 761P0000929 0.707061386E+02, 0.000000000E+00, 0.707041473E+02, 761P0000930 0.530297458E+00; 761P0000931 124, 0.150814921E+00, 0.988561988E+00, 0.000000000E+00, 763P0000932 0.561105919E+01,-0.988561988E+00, 0.150814921E+00, 763P0000933 0.000000000E+00, 0.809846725E+02, 0.000000000E+00, 763P0000934 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 763P0000935


UNCLASSIFIED 97

100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 765P0000936 0.682230606E+02, 0.000000000E+00, 0.682210007E+02, 765P0000937 0.530266106E+00; 765P0000938 124, 0.158631563E+00, 0.987337768E+00, 0.000000000E+00, 767P0000939 0.598047256E+01,-0.987337768E+00, 0.158631563E+00, 767P0000940 0.000000000E+00, 0.786254883E+02, 0.000000000E+00, 767P0000941 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 767P0000942 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 769P0000943 0.658351517E+02, 0.000000000E+00, 0.658330154E+02, 769P0000944 0.530340254E+00; 769P0000945 124, 0.166727036E+00, 0.986003041E+00, 0.000000000E+00, 771P0000946 0.635730791E+01,-0.986003041E+00, 0.166727036E+00, 771P0000947 0.000000000E+00, 0.763380508E+02, 0.000000000E+00, 771P0000948 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 771P0000949 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 773P0000950 0.635169029E+02, 0.000000000E+00, 0.635146866E+02, 773P0000951 0.530381024E+00; 773P0000952 124, 0.175103992E+00, 0.984549940E+00, 0.000000000E+00, 775P0000953 0.674511337E+01,-0.984549940E+00, 0.175103992E+00, 775P0000954 0.000000000E+00, 0.741025085E+02, 0.000000000E+00, 775P0000955 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 775P0000956 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 777P0000957 0.612479897E+02, 0.000000000E+00, 0.612456932E+02, 777P0000958 0.530547261E+00; 777P0000959 124, 0.183823645E+00, 0.982959270E+00, 0.000000000E+00, 779P0000960 0.723188972E+01,-0.982959270E+00, 0.183823645E+00, 779P0000961 0.000000000E+00, 0.714325333E+02, 0.000000000E+00, 779P0000962 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 779P0000963 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 781P0000964 0.585340309E+02, 0.000000000E+00, 0.585316238E+02, 781P0000965 0.530711532E+00; 781P0000966 124, 0.192956552E+00, 0.981207252E+00, 0.000000000E+00, 783P0000967 0.776327515E+01,-0.981207252E+00, 0.192956552E+00, 783P0000968 0.000000000E+00, 0.686598053E+02, 0.000000000E+00, 783P0000969 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 783P0000970 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 785P0000971 0.557108765E+02, 0.000000000E+00, 0.557083473E+02, 785P0000972 0.530869305E+00; 785P0000973 124, 0.202457145E+00, 0.979291081E+00, 0.000000000E+00, 787P0000974 0.813110828E+01,-0.979291081E+00, 0.202457145E+00, 787P0000975 0.000000000E+00, 0.668357925E+02, 0.000000000E+00, 787P0000976 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 787P0000977 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 789P0000978 0.538501625E+02, 0.000000000E+00, 0.538475418E+02, 789P0000979 0.531160116E+00; 789P0000980 124, 0.212293178E+00, 0.977205992E+00, 0.000000000E+00, 791P0000981 0.854784775E+01,-0.977205992E+00, 0.212293178E+00, 791P0000982 0.000000000E+00, 0.648690948E+02, 0.000000000E+00, 791P0000983 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 791P0000984 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 793P0000985 0.518398247E+02, 0.000000000E+00, 0.518371010E+02, 793P0000986 0.531535447E+00; 793P0000987 124, 0.222546145E+00, 0.974922121E+00, 0.000000000E+00, 795P0000988 0.907371902E+01,-0.974922121E+00, 0.222546145E+00, 795P0000989 0.000000000E+00, 0.625069771E+02, 0.000000000E+00, 795P0000990 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 795P0000991 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 797P0000992 0.494199104E+02, 0.000000000E+00, 0.494170456E+02, 797P0000993 0.532081842E+00; 797P0000994 124, 0.233307242E+00, 0.972403049E+00, 0.000000000E+00, 799P0000995


UNCLASSIFIED 98

0.963722801E+01,-0.972403049E+00, 0.233307242E+00, 799P0000996 0.000000000E+00, 0.600978851E+02, 0.000000000E+00, 799P0000997 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 799P0000998 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 801P0000999 0.469458313E+02, 0.000000000E+00, 0.469428101E+02, 801P0001000 0.532604277E+00; 801P0001001 124, 0.244599625E+00, 0.969624162E+00, 0.000000000E+00, 803P0001002 0.101752977E+02,-0.969624162E+00, 0.244599625E+00, 803P0001003 0.000000000E+00, 0.579103966E+02, 0.000000000E+00, 803P0001004 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 803P0001005 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 805P0001006 0.446931725E+02, 0.000000000E+00, 0.446899872E+02, 805P0001007 0.533509910E+00; 805P0001008 124, 0.256471872E+00, 0.966551661E+00, 0.000000000E+00, 807P0001009 0.107499065E+02,-0.966551661E+00, 0.256471872E+00, 807P0001010 0.000000000E+00, 0.556880913E+02, 0.000000000E+00, 807P0001011 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 807P0001012 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 809P0001013 0.423978271E+02, 0.000000000E+00, 0.423944626E+02, 809P0001014 0.534201264E+00; 809P0001015 124, 0.268965244E+00, 0.963149846E+00, 0.000000000E+00, 811P0001016 0.113386002E+02,-0.963149846E+00, 0.268965244E+00, 811P0001017 0.000000000E+00, 0.535251122E+02, 0.000000000E+00, 811P0001018 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 811P0001019 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 813P0001020 0.401562157E+02, 0.000000000E+00, 0.401526413E+02, 813P0001021 0.535668135E+00; 813P0001022 124, 0.282220095E+00, 0.959349692E+00, 0.000000000E+00, 815P0001023 0.120343008E+02,-0.959349692E+00, 0.282220095E+00, 815P0001024 0.000000000E+00, 0.510963402E+02, 0.000000000E+00, 815P0001025 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 815P0001026 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 817P0001027 0.376298256E+02, 0.000000000E+00, 0.376259956E+02, 817P0001028 0.536804378E+00; 817P0001029 124, 0.296602249E+00, 0.955001175E+00, 0.000000000E+00, 819P0001030 0.130788164E+02,-0.955001175E+00, 0.296602249E+00, 819P0001031 0.000000000E+00, 0.476368561E+02, 0.000000000E+00, 819P0001032 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 819P0001033 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 821P0001034 0.340161972E+02, 0.000000000E+00, 0.340119286E+02, 821P0001035 0.538877487E+00; 821P0001036 124, 0.312638760E+00, 0.949872136E+00, 0.000000000E+00, 823P0001037 0.142352438E+02,-0.949872136E+00, 0.312638760E+00, 823P0001038 0.000000000E+00, 0.440151443E+02, 0.000000000E+00, 823P0001039 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 823P0001040 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 825P0001041 0.302144737E+02, 0.000000000E+00, 0.302096310E+02, 825P0001042 0.540935993E+00; 825P0001043 124, 0.330082536E+00, 0.943952024E+00, 0.000000000E+00, 827P0001044 0.147639046E+02,-0.943952024E+00, 0.330082536E+00, 827P0001045 0.000000000E+00, 0.424559784E+02, 0.000000000E+00, 827P0001046 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 827P0001047 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 829P0001048 0.285681915E+02, 0.000000000E+00, 0.285629883E+02, 829P0001049 0.545230806E+00; 829P0001050 124, 0.348793656E+00, 0.937199533E+00, 0.000000000E+00, 831P0001051 0.155191956E+02,-0.937199533E+00, 0.348793656E+00, 831P0001052 0.000000000E+00, 0.403605003E+02, 0.000000000E+00, 831P0001053 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 831P0001054 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 833P0001055


UNCLASSIFIED 99

0.263408604E+02, 0.000000000E+00, 0.263340816E+02, 833P0001056 0.597594678E+00; 833P0001057 124, 0.372392148E+00, 0.928075433E+00, 0.000000000E+00, 835P0001058 0.172910271E+02,-0.928075433E+00, 0.372392148E+00, 835P0001059 0.000000000E+00, 0.357599373E+02, 0.000000000E+00, 835P0001060 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 835P0001061 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 837P0001062 0.214112854E+02, 0.000000000E+00, 0.214029160E+02, 837P0001063 0.598626614E+00; 837P0001064 124, 0.399758697E+00, 0.916620433E+00, 0.000000000E+00, 839P0001065 0.181879539E+02,-0.916620433E+00, 0.399758697E+00, 839P0001066 0.000000000E+00, 0.336119576E+02, 0.000000000E+00, 839P0001067 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 839P0001068 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 841P0001069 0.190838165E+02, 0.000000000E+00, 0.190744247E+02, 841P0001070 0.598606229E+00; 841P0001071 124, 0.428453296E+00, 0.903563917E+00, 0.000000000E+00, 843P0001072 0.182654171E+02,-0.903563917E+00, 0.428453296E+00, 843P0001073 0.000000000E+00, 0.334417191E+02, 0.000000000E+00, 843P0001074 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 843P0001075 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 845P0001076 0.188968067E+02, 0.000000000E+00, 0.188873234E+02, 845P0001077 0.598559320E+00; 845P0001078 124, 0.456381321E+00, 0.889784276E+00, 0.000000000E+00, 847P0001079 0.179720764E+02,-0.889784276E+00, 0.456381321E+00, 847P0001080 0.000000000E+00, 0.340358543E+02, 0.000000000E+00, 847P0001081 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 847P0001082 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 849P0001083 0.195593319E+02, 0.000000000E+00, 0.195501728E+02, 849P0001084 0.598496556E+00; 849P0001085 124, 0.483358979E+00, 0.875422180E+00, 0.000000000E+00, 851P0001086 0.179488087E+02,-0.875422180E+00, 0.483358979E+00, 851P0001087 0.000000000E+00, 0.340796204E+02, 0.000000000E+00, 851P0001088 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 851P0001089 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 853P0001090 0.196088924E+02, 0.000000000E+00, 0.195997601E+02, 853P0001091 0.598419368E+00; 853P0001092 124, 0.509927571E+00, 0.860217273E+00, 0.000000000E+00, 855P0001093 0.180050411E+02,-0.860217273E+00, 0.509927571E+00, 855P0001094 0.000000000E+00, 0.339812813E+02, 0.000000000E+00, 855P0001095 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 855P0001096 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 857P0001097 0.194956245E+02, 0.000000000E+00, 0.194864407E+02, 857P0001098 0.598330915E+00; 857P0001099 124, 0.536132812E+00, 0.844133675E+00, 0.000000000E+00, 859P0001100 0.180414104E+02,-0.844133675E+00, 0.536132812E+00, 859P0001101 0.000000000E+00, 0.339220848E+02, 0.000000000E+00, 859P0001102 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 859P0001103 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 861P0001104 0.194261551E+02, 0.000000000E+00, 0.194169426E+02, 861P0001105 0.598240674E+00; 861P0001106 124, 0.561918974E+00, 0.827192247E+00, 0.000000000E+00, 863P0001107 0.180765667E+02,-0.827192247E+00, 0.561918974E+00, 863P0001108 0.000000000E+00, 0.338684578E+02, 0.000000000E+00, 863P0001109 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 863P0001110 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 865P0001111 0.193620415E+02, 0.000000000E+00, 0.193528004E+02, 865P0001112 0.598142147E+00; 865P0001113 124, 0.587243080E+00, 0.809410632E+00, 0.000000000E+00, 867P0001114 0.181114655E+02,-0.809410632E+00, 0.587243080E+00, 867P0001115


UNCLASSIFIED 100

0.000000000E+00, 0.338187981E+02, 0.000000000E+00, 867P0001116 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 867P0001117 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 869P0001118 0.193013515E+02, 0.000000000E+00, 0.192920837E+02, 869P0001119 0.598043621E+00; 869P0001120 124, 0.612073839E+00, 0.790800631E+00, 0.000000000E+00, 871P0001121 0.181444073E+02,-0.790800631E+00, 0.612073839E+00, 871P0001122 0.000000000E+00, 0.337749023E+02, 0.000000000E+00, 871P0001123 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 871P0001124 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 873P0001125 0.192464752E+02, 0.000000000E+00, 0.192371845E+02, 873P0001126 0.597949743E+00; 873P0001127 124, 0.636382818E+00, 0.771373391E+00, 0.000000000E+00, 875P0001128 0.181777096E+02,-0.771373391E+00, 0.636382818E+00, 875P0001129 0.000000000E+00, 0.337331314E+02, 0.000000000E+00, 875P0001130 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 875P0001131 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 877P0001132 0.191930618E+02, 0.000000000E+00, 0.191837482E+02, 877P0001133 0.597846568E+00; 877P0001134 124, 0.660125256E+00, 0.751155496E+00, 0.000000000E+00, 879P0001135 0.182056580E+02,-0.751155496E+00, 0.660125256E+00, 879P0001136 0.000000000E+00, 0.337004128E+02, 0.000000000E+00, 879P0001137 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 879P0001138 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 881P0001139 0.191500359E+02, 0.000000000E+00, 0.191407051E+02, 881P0001140 0.597756386E+00; 881P0001141 124, 0.683275998E+00, 0.730160236E+00, 0.000000000E+00, 883P0001142 0.182317638E+02,-0.730160236E+00, 0.683275998E+00, 883P0001143 0.000000000E+00, 0.336715355E+02, 0.000000000E+00, 883P0001144 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 883P0001145 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 885P0001146 0.191111126E+02, 0.000000000E+00, 0.191017647E+02, 885P0001147 0.597673476E+00; 885P0001148 124, 0.705792785E+00, 0.708418369E+00, 0.000000000E+00, 887P0001149 0.182517586E+02,-0.708418369E+00, 0.705792785E+00, 887P0001150 0.000000000E+00, 0.336508446E+02, 0.000000000E+00, 887P0001151 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 887P0001152 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 889P0001153 0.190823421E+02, 0.000000000E+00, 0.190729828E+02, 889P0001154 0.597590864E+00; 889P0001155 124, 0.727642298E+00, 0.685956776E+00, 0.000000000E+00, 891P0001156 0.182694874E+02,-0.685956776E+00, 0.727642298E+00, 891P0001157 0.000000000E+00, 0.336337280E+02, 0.000000000E+00, 891P0001158 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 891P0001159 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 893P0001160 0.190577011E+02, 0.000000000E+00, 0.190483322E+02, 893P0001161 0.597522318E+00; 893P0001162 124, 0.748799860E+00, 0.662796199E+00, 0.000000000E+00, 895P0001163 0.182772903E+02,-0.662796199E+00, 0.748799860E+00, 895P0001164 0.000000000E+00, 0.336265030E+02, 0.000000000E+00, 895P0001165 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 895P0001166 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 897P0001167 0.190470695E+02, 0.000000000E+00, 0.190376968E+02, 897P0001168 0.597468495E+00; 897P0001169 124, 0.769229412E+00, 0.638972759E+00, 0.000000000E+00, 899P0001170 0.182826519E+02,-0.638972759E+00, 0.769229412E+00, 899P0001171 0.000000000E+00, 0.336217613E+02, 0.000000000E+00, 899P0001172 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 899P0001173 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 901P0001174 0.190399151E+02, 0.000000000E+00, 0.190305405E+02, 901P0001175


UNCLASSIFIED 101

0.597413242E+00; 901P0001176 124, 0.788891554E+00, 0.614532351E+00, 0.000000000E+00, 903P0001177 0.182772427E+02,-0.614532351E+00, 0.788891554E+00, 903P0001178 0.000000000E+00, 0.336262894E+02, 0.000000000E+00, 903P0001179 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 903P0001180 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 905P0001181 0.190469666E+02, 0.000000000E+00, 0.190375957E+02, 905P0001182 0.597382188E+00; 905P0001183 124, 0.807772756E+00, 0.589494050E+00, 0.000000000E+00, 907P0001184 0.182669277E+02,-0.589494050E+00, 0.807772756E+00, 907P0001185 0.000000000E+00, 0.336340065E+02, 0.000000000E+00, 907P0001186 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 907P0001187 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 909P0001188 0.190598469E+02, 0.000000000E+00, 0.190504837E+02, 909P0001189 0.597361803E+00; 909P0001190 124, 0.825835884E+00, 0.563910604E+00, 0.000000000E+00, 911P0001191 0.182439518E+02,-0.563910604E+00, 0.825835884E+00, 911P0001192 0.000000000E+00, 0.336503334E+02, 0.000000000E+00, 911P0001193 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 911P0001194 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 913P0001195 0.190880280E+02, 0.000000000E+00, 0.190786800E+02, 913P0001196 0.597352207E+00; 913P0001197 124, 0.843068421E+00, 0.537806392E+00, 0.000000000E+00, 915P0001198 0.182167320E+02,-0.537806392E+00, 0.843068421E+00, 915P0001199 0.000000000E+00, 0.336681328E+02, 0.000000000E+00, 915P0001200 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 915P0001201 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 917P0001202 0.191205482E+02, 0.000000000E+00, 0.191112137E+02, 917P0001203 0.597354531E+00; 917P0001204 124, 0.859436572E+00, 0.511242449E+00, 0.000000000E+00, 919P0001205 0.181784096E+02,-0.511242449E+00, 0.859436572E+00, 919P0001206 0.000000000E+00, 0.336918945E+02, 0.000000000E+00, 919P0001207 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 919P0001208 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 921P0001209 0.191656322E+02, 0.000000000E+00, 0.191563206E+02, 921P0001210 0.597369730E+00; 921P0001211 124, 0.874937057E+00, 0.484236747E+00, 0.000000000E+00, 923P0001212 0.181342068E+02,-0.484236747E+00, 0.874937057E+00, 923P0001213 0.000000000E+00, 0.337171173E+02, 0.000000000E+00, 923P0001214 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 923P0001215 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 925P0001216 0.192165203E+02, 0.000000000E+00, 0.192072315E+02, 925P0001217 0.597387373E+00; 925P0001218 124, 0.889539778E+00, 0.456857592E+00, 0.000000000E+00, 927P0001219 0.180767059E+02,-0.456857592E+00, 0.889539778E+00, 927P0001220 0.000000000E+00, 0.337479668E+02, 0.000000000E+00, 927P0001221 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 927P0001222 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 929P0001223 0.192817650E+02, 0.000000000E+00, 0.192725067E+02, 929P0001224 0.597421765E+00; 929P0001225 124, 0.903245151E+00, 0.429124892E+00, 0.000000000E+00, 931P0001226 0.180153923E+02,-0.429124892E+00, 0.903245151E+00, 931P0001227 0.000000000E+00, 0.337782288E+02, 0.000000000E+00, 931P0001228 0.000000000E+00, 0.100000000E+01, 0.000000000E+00; 931P0001229 100, 0.000000000E+00, 0.000000000E+00, 0.000000000E+00, 933P0001230 0.193501320E+02, 0.000000000E+00, 0.193409061E+02, 933P0001231 0.597457588E+00; 933P0001232 124, 0.916041732E+00, 0.401082873E+00, 0.000000000E+00, 935P0001233 0.179433689E+02,-0.401082873E+00, 0.916041732E+00, 935P0001234 0.000000000E+00, 0.338109474E+02, 0.000000000E+00, 935P0001235


UNCLASSIFIED 102

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Page classification: UNCLASSIFIED

DEFENCE SCIENCE AND TECHNOLOGY GROUP

DOCUMENT CONTROL DATA 1. DLM/CAVEAT (OF DOCUMENT)

2. TITLE A Modified Constant-Stress Coupon for Enhanced Natural Crack Start during Fatigue Testing

3. SECURITY CLASSIFICATION (FOR UNCLASSIFIED REPORTS THAT ARE LIMITED RELEASE USE (L) NEXT TO DOCUMENT CLASSIFICATION) Document (U) Title (U) Abstract (U)

4. AUTHOR(S) Witold Waldman, Robert Kaye and Xiaobo Yu

5. CORPORATE AUTHOR Defence Science and Technology Group 506 Lorimer St Fishermans Bend Victoria 3207 Australia

6a. DST GROUP NUMBER DST-Group-TR-3252

6b. AR NUMBER AR-016-590

6c. TYPE OF REPORT Technical Report

7. DOCUMENT DATE May 2016

8. OBJECTIVE FOLDER ID fAV1044714

9. TASK NUMBER AIR 07/283

10. TASK SPONSOR OIC-ASI-DGTA

11. NO. OF PAGES 95

12. NO. OF REFERENCES 33

13. DST GROUP PUBLICATIONS REPOSITORY http://dspace.dsto.defence.gov.au/dspace/

14. RELEASE AUTHORITY Chief, Aerospace Division

15. SECONDARY RELEASE STATEMENT OF THIS DOCUMENT

Approved for public release OVERSEAS ENQUIRIES OUTSIDE STATED LIMITATIONS SHOULD BE REFERRED THROUGH DOCUMENT EXCHANGE, PO BOX 1500, EDINBURGH, SA 5111 16. DELIBERATE ANNOUNCEMENT No Limitations 17. CITATION IN OTHER DOCUMENTS Yes 18. RESEARCH LIBRARY THESAURUS Shape optimisation, Stress concentration, Fatigue testing, Constant-stress coupon, Fatigue coupon, Stress intensity factor, Fillet, Notch analysis, Finite element analysis, Boundary element analysis, Natural crack start, Beta factors 19. ABSTRACT This report details the development of a modified constant-stress coupon for use in fatigue testing. This novel coupon design has a significantly greater surface area along the notch boundary that is subjected to the peak stress, and it is useful in studies of the probabilistic growth of in-service fatigue cracks where fatigue life is governed by the most severe defect. The extended region of uniform stress is achieved by shape optimisation of the notch boundary, resulting in the elimination of the highly-localised stress concentration that is a characteristic feature of a traditional dog-bone coupon. The presence of an extensive region of uniform stress increases the incidence of fatigue cracking from small naturally-occurring surface imperfections or discontinuities, as well as more uniformly distributing the fatigue cracking over the region of constant stress. Stress intensity factors have also been computed for simulated crack growth trajectories for edge cracks starting at various locations distributed along the notch boundary. Use of the constant-stress coupon reduces the number of coupons that need to be tested in order to attain desired statistical confidence levels, leading to significant time savings and greatly reduced costs in conducting fatigue testing programs studying the initiation and growth behaviour of small cracks.

Page classification: UNCLASSIFIED

A Modified Constant-Stress Coupon for Enhanced Natural ... · A Modified Constant-Stress Coupon for Enhanced Natural Crack Start during Fatigue Testing Executive Summary The Structural

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